Rational and Nearly Rational Varieties

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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 Curves on Algebraic Varieties

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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

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Publisher :
ISBN 13 : 9781107471740
Total Pages : pages
Book Rating : 4.4/5 (717 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 . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rational Points on Varieties

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 1470437732
Total Pages : 358 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 Soc.. This book was released on 2017-12-13 with total page 358 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.

Rational Points on Algebraic Varieties

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Author :
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.

Rationality Problems in Algebraic Geometry

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Publisher : Springer
ISBN 13 : 3319462091
Total Pages : 176 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Rationality Problems in Algebraic Geometry by : Arnaud Beauville

Download or read book Rationality Problems in Algebraic Geometry written by Arnaud Beauville and published by Springer. This book was released on 2016-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

The Collected Papers of Wei-Liang Chow

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Publisher : World Scientific
ISBN 13 : 9812776923
Total Pages : 522 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis The Collected Papers of Wei-Liang Chow by : Shiing-Shen Chern

Download or read book The Collected Papers of Wei-Liang Chow written by Shiing-Shen Chern and published by World Scientific. This book was released on 2002 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."

Higher-Dimensional Algebraic Geometry

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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.

Birational Geometry of Algebraic Varieties

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Publisher : Cambridge University Press
ISBN 13 : 9780511662560
Total Pages : 254 pages
Book Rating : 4.6/5 (625 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 2010-03-24 with total page 254 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.

Ample Subvarieties of Algebraic Varieties

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Publisher : Springer
ISBN 13 : 3540363459
Total Pages : 271 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Ample Subvarieties of Algebraic Varieties by : Robin Hartshorne

Download or read book Ample Subvarieties of Algebraic Varieties written by Robin Hartshorne and published by Springer. This book was released on 2006-11-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Concise Introduction to Algebraic Varieties

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470466651
Total Pages : 259 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Concise Introduction to Algebraic Varieties by : Brian Osserman

Download or read book A Concise Introduction to Algebraic Varieties written by Brian Osserman and published by American Mathematical Society. This book was released on 2021-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis and Algebraic Geometry

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Author :
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.

How Reason Almost Lost Its Mind

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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.

Rational Ritual

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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.

Geometry of Higher Dimensional Algebraic Varieties

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Publisher : Springer Science & Business Media
ISBN 13 : 9783764354909
Total Pages : 228 pages
Book Rating : 4.3/5 (549 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 Springer Science & Business Media. This book was released on 1997-03-20 with total page 228 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.

Introduction to Algebraic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 1470435187
Total Pages : 498 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Algebraic Geometry by : Steven Dale Cutkosky

Download or read book Introduction to Algebraic Geometry written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Torsors and Rational Points

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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.