Rational And Nearly Rational Varieties

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Rational and Nearly Rational Varieties

Author : János Kollár
Publisher : Cambridge University Press
ISBN 13 : 9780521832076
Total Pages : 246 pages
Book Rating : 4.8/5 (32 download)

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Book Synopsis Rational and Nearly Rational Varieties by : János Kollár

Download or read book Rational and Nearly Rational Varieties written by János Kollár and published by Cambridge University Press. This book was released on 2004-04-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

Rational Points on Varieties

Author : Bjorn Poonen
Publisher : American Mathematical Society
ISBN 13 : 1470474581
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Rational Points on Varieties by : Bjorn Poonen

Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Society. This book was released on 2023-08-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University

Rational Curves on Algebraic Varieties

Author : Janos Kollar
Publisher : Springer Science & Business Media
ISBN 13 : 3662032767
Total Pages : 330 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Rational Curves on Algebraic Varieties by : Janos Kollar

Download or read book Rational Curves on Algebraic Varieties written by Janos Kollar and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.

Rational and Nearly Rational Varieties ICM Edition

Author : Kollar
Publisher :
ISBN 13 : 9780521168878
Total Pages : pages
Book Rating : 4.1/5 (688 download)

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Book Synopsis Rational and Nearly Rational Varieties ICM Edition by : Kollar

Download or read book Rational and Nearly Rational Varieties ICM Edition written by Kollar and published by . This book was released on 2010-07-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rationality of Varieties

Author : Gavril Farkas
Publisher : Springer Nature
ISBN 13 : 3030754219
Total Pages : 433 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Rationality of Varieties by : Gavril Farkas

Download or read book Rationality of Varieties written by Gavril Farkas and published by Springer Nature. This book was released on 2021-10-19 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

Rational Points on Algebraic Varieties

Author : Emmanuel Peyre
Publisher : Birkhäuser
ISBN 13 : 3034883684
Total Pages : 455 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Rational Points on Algebraic Varieties by : Emmanuel Peyre

Download or read book Rational Points on Algebraic Varieties written by Emmanuel Peyre and published by Birkhäuser. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.

Torsors and Rational Points

Author : Alexei Skorobogatov
Publisher : Cambridge University Press
ISBN 13 : 0521802377
Total Pages : 197 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Torsors and Rational Points by : Alexei Skorobogatov

Download or read book Torsors and Rational Points written by Alexei Skorobogatov and published by Cambridge University Press. This book was released on 2001-07-05 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.

Predictably Rational?

Author : Richard B. McKenzie
Publisher : Springer Science & Business Media
ISBN 13 : 3642015867
Total Pages : 308 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Predictably Rational? by : Richard B. McKenzie

Download or read book Predictably Rational? written by Richard B. McKenzie and published by Springer Science & Business Media. This book was released on 2009-10-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mainstream economists everywhere exhibit an "irrational passion for dispassionate rationality." Behavioral economists, and long-time critic of mainstream economics suggests that people in mainstrean economic models "can think like Albert Einstein, store as much memory as IBM’s Big Blue, and exercise the will power of Mahatma Gandhi," suggesting that such a view of real world modern homo sapiens is simply wrongheaded. Indeed, Thaler and other behavioral economists and psychology have documented a variety of ways in which real-world people fall far short of mainstream economists' idealized economic actor, perfectly rational homo economicus. Behavioral economist Daniel Ariely has concluded that real-world people not only exhibit an array of decision-making frailties and biases, they are "predictably irrational," a position now shared by so many behavioral economists, psychologists, sociologists, and evolutionary biologists that a defense of the core rationality premise of modedrn economics is demanded.

Rational Ritual

Author : Michael Suk-Young Chwe
Publisher : Princeton University Press
ISBN 13 : 0691158282
Total Pages : 152 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Rational Ritual by : Michael Suk-Young Chwe

Download or read book Rational Ritual written by Michael Suk-Young Chwe and published by Princeton University Press. This book was released on 2013-04-28 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Why do beer commercials dominate Super Bowl advertising? How do political ceremonies establish authority? Why were circular forms favored for public festivals during the French Revolution? This book answers these questions using a single concept: common knowledge. Game theory shows that in order to coordinate its actions, a group of people must form "common knowledge." Each person wants to participate only if others also participate. Members must have knowledge of each other, knowledge of that knowledge, and so on. Michael Chwe applies this insight, with striking erudition, to analyze a range of rituals across history and cultures. He shows that public ceremonies are powerful not simply because they transmit meaning from a central source to each audience member but because they let audience members know what other members know. In a new afterword, Chwe delves into new applications of common knowledge, both in the real world and in experiments, and considers how generating common knowledge has become easier in the digital age." -- From the jacket.

Foliation Theory in Algebraic Geometry

Author : Paolo Cascini
Publisher : Springer
ISBN 13 : 3319244604
Total Pages : 216 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Foliation Theory in Algebraic Geometry by : Paolo Cascini

Download or read book Foliation Theory in Algebraic Geometry written by Paolo Cascini and published by Springer. This book was released on 2016-03-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

How Reason Almost Lost Its Mind

Author : Paul Erickson
Publisher : University of Chicago Press
ISBN 13 : 022604677X
Total Pages : 268 pages
Book Rating : 4.2/5 (26 download)

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Book Synopsis How Reason Almost Lost Its Mind by : Paul Erickson

Download or read book How Reason Almost Lost Its Mind written by Paul Erickson and published by University of Chicago Press. This book was released on 2013-11-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the United States at the height of the Cold War, roughly between the end of World War II and the early 1980s, a new project of redefining rationality commanded the attention of sharp minds, powerful politicians, wealthy foundations, and top military brass. Its home was the human sciences—psychology, sociology, political science, and economics, among others—and its participants enlisted in an intellectual campaign to figure out what rationality should mean and how it could be deployed. How Reason Almost Lost Its Mind brings to life the people—Herbert Simon, Oskar Morgenstern, Herman Kahn, Anatol Rapoport, Thomas Schelling, and many others—and places, including the RAND Corporation, the Center for Advanced Study in the Behavioral Sciences, the Cowles Commission for Research and Economics, and the Council on Foreign Relations, that played a key role in putting forth a “Cold War rationality.” Decision makers harnessed this picture of rationality—optimizing, formal, algorithmic, and mechanical—in their quest to understand phenomena as diverse as economic transactions, biological evolution, political elections, international relations, and military strategy. The authors chronicle and illuminate what it meant to be rational in the age of nuclear brinkmanship.

Birational Geometry of Algebraic Varieties

Author : Janos Kollár
Publisher : Cambridge University Press
ISBN 13 : 9780521060226
Total Pages : 264 pages
Book Rating : 4.0/5 (62 download)

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Book Synopsis Birational Geometry of Algebraic Varieties by : Janos Kollár

Download or read book Birational Geometry of Algebraic Varieties written by Janos Kollár and published by Cambridge University Press. This book was released on 2008-02-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Higher-Dimensional Algebraic Geometry

Author : Olivier Debarre
Publisher : Springer Science & Business Media
ISBN 13 : 147575406X
Total Pages : 245 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Higher-Dimensional Algebraic Geometry by : Olivier Debarre

Download or read book Higher-Dimensional Algebraic Geometry written by Olivier Debarre and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.

Complex Analysis and Algebraic Geometry

Author : Kunihiko Kodaira
Publisher : CUP Archive
ISBN 13 : 9780521217774
Total Pages : 424 pages
Book Rating : 4.2/5 (177 download)

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Book Synopsis Complex Analysis and Algebraic Geometry by : Kunihiko Kodaira

Download or read book Complex Analysis and Algebraic Geometry written by Kunihiko Kodaira and published by CUP Archive. This book was released on 1977 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Geometry of Higher Dimensional Algebraic Varieties

Author : Thomas Peternell
Publisher : Birkhäuser
ISBN 13 : 3034888937
Total Pages : 221 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Geometry of Higher Dimensional Algebraic Varieties by : Thomas Peternell

Download or read book Geometry of Higher Dimensional Algebraic Varieties written by Thomas Peternell and published by Birkhäuser. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Cox Rings

Author : Ivan Arzhantsev
Publisher : Cambridge University Press
ISBN 13 : 1107024625
Total Pages : 539 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Cox Rings by : Ivan Arzhantsev

Download or read book Cox Rings written by Ivan Arzhantsev and published by Cambridge University Press. This book was released on 2015 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

Rational Points and Arithmetic of Fundamental Groups

Author : Jakob Stix
Publisher : Springer
ISBN 13 : 3642306748
Total Pages : 249 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Rational Points and Arithmetic of Fundamental Groups by : Jakob Stix

Download or read book Rational Points and Arithmetic of Fundamental Groups written by Jakob Stix and published by Springer. This book was released on 2012-10-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.