Birational Geometry of Algebraic Varieties

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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.

Birational Geometry and Moduli Spaces

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Publisher : Springer Nature
ISBN 13 : 303037114X
Total Pages : 200 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Birational Geometry and Moduli Spaces by : Elisabetta Colombo

Download or read book Birational Geometry and Moduli Spaces written by Elisabetta Colombo and published by Springer Nature. This book was released on 2020-02-25 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Birational Geometry of Foliations

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Publisher : Springer
ISBN 13 : 3319143107
Total Pages : 140 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Birational Geometry of Foliations by : Marco Brunella

Download or read book Birational Geometry of Foliations written by Marco Brunella and published by Springer. This book was released on 2015-03-25 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text presents the birational classification of holomorphic foliations of surfaces. It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces in the spirit of the classification of complex algebraic surfaces.

Birational Geometry, Rational Curves, and Arithmetic

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Publisher : Springer Science & Business Media
ISBN 13 : 146146482X
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Birational Geometry, Rational Curves, and Arithmetic by : Fedor Bogomolov

Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Algebraic Geometry

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Publisher : Springer
ISBN 13 : 9781461381211
Total Pages : 357 pages
Book Rating : 4.3/5 (812 download)

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Book Synopsis Algebraic Geometry by : S. Iitaka

Download or read book Algebraic Geometry written by S. Iitaka and published by Springer. This book was released on 2011-10-14 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties. This volume grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo, in 1977. While writing this English version, the author has tried to rearrange and rewrite the original material so that even beginners can read it easily without referring to other books, such as textbooks on commutative algebra. The reader is only expected to know the definition of Noetherin rings and the statement of the Hilbert basis theorem. The new chapters 1, 2, and 10 have been expanded. In particular, the exposition of D-dimension theory, although shorter, is more complete than in the old version. However, to keep the book of manageable size, the latter parts of Chapters 6, 9, and 11 have been removed. I thank Mr. A. Sevenster for encouraging me to write this new version, and Professors K. K. Kubota in Kentucky and P. M. H. Wilson in Cam bridge for their careful and critical reading of the English manuscripts and typescripts. I held seminars based on the material in this book at The University of Tokyo, where a large number of valuable comments and suggestions were given by students Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.

Automorphisms in Birational and Affine Geometry

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Publisher : Springer
ISBN 13 : 3319056816
Total Pages : 509 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Automorphisms in Birational and Affine Geometry by : Ivan Cheltsov

Download or read book Automorphisms in Birational and Affine Geometry written by Ivan Cheltsov and published by Springer. This book was released on 2014-06-11 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.

Birational Geometry of Hypersurfaces

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Publisher : Springer Nature
ISBN 13 : 3030186385
Total Pages : 297 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Birational Geometry of Hypersurfaces by : Andreas Hochenegger

Download or read book Birational Geometry of Hypersurfaces written by Andreas Hochenegger and published by Springer Nature. This book was released on 2019-10-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

The Birational Geometry of Degenerations

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Author :
Publisher : Birkhauser
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Birational Geometry of Degenerations by : Robert Friedman

Download or read book The Birational Geometry of Degenerations written by Robert Friedman and published by Birkhauser. This book was released on 1983 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Geometry

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Publisher :
ISBN 13 : 9783540905462
Total Pages : 357 pages
Book Rating : 4.9/5 (54 download)

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Book Synopsis Algebraic Geometry by : Shigeru Iitaka

Download or read book Algebraic Geometry written by Shigeru Iitaka and published by . This book was released on 1982 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 1475738498
Total Pages : 511 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Algebraic Geometry by : Robin Hartshorne

Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Algebraic Geometry for Scientists and Engineers

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Publisher : American Mathematical Soc.
ISBN 13 : 0821815350
Total Pages : 295 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Geometry for Scientists and Engineers by : Shreeram Shankar Abhyankar

Download or read book Algebraic Geometry for Scientists and Engineers written by Shreeram Shankar Abhyankar and published by American Mathematical Soc.. This book was released on 1990 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced undergraduates in mathematics. In addition to providing a concrete or algorithmic approach to algebraic geometry, the author also attempts to motivate and explain its link to more modern algebraic geometry based on abstract algebra.The book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities. The emphasis is on presenting heuristic ideas and suggestive arguments rather than formal proofs. Readers will gain new insight into the subject of algebraic geometry in a way that should increase appreciation of modern treatments of the subject, as well as enhance its utility in applications in science and industry.

Birational Algebraic Geometry

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821807692
Total Pages : 152 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Birational Algebraic Geometry by : Yujiro Kawamata

Download or read book Birational Algebraic Geometry written by Yujiro Kawamata and published by American Mathematical Soc.. This book was released on 1997 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work, intended for research mathematicians, presents proceedings from the Japan-US Mathematics Institute (JAMI) Conference on Birational Algebraic Geometry in memory of Wei-Liang Chow, held at the John's Hopkins University in Baltimore in April 1996. These proceedings bring to light the many directions in which birational algebraic geometry is headed. Featured are: problems on special models, such as Fanos and their fibrations; adjunctions and subadjunction formulae; projectivity and projective embeddings; and more. Some papers reflect the frontiers of this rapidly-developing area of mathematics. Therefore, in these cases, only directions are given without complete explanations or proofs.

Algebraic Groups and Their Birational Invariants

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821872885
Total Pages : 234 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Groups and Their Birational Invariants by : V. E. Voskresenskii

Download or read book Algebraic Groups and Their Birational Invariants written by V. E. Voskresenskii and published by American Mathematical Soc.. This book was released on 2011-10-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Algebraic Geometry and Topology

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Publisher : Princeton University Press
ISBN 13 : 1400879914
Total Pages : 410 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Algebraic Geometry and Topology by : Ralph Hartzler Fox

Download or read book Algebraic Geometry and Topology written by Ralph Hartzler Fox and published by Princeton University Press. This book was released on 2015-12-08 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the developments of modern algebraic geometry and topology stem from the ideas of S. Lefschetz. These are featured in this volume of contemporary research papers contributed by mathematical colleagues to celebrate his seventieth birthday. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Algebraic Geometry

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Publisher : Springer
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Algebraic Geometry by : S. Iitaka

Download or read book Algebraic Geometry written by S. Iitaka and published by Springer. This book was released on 1982 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties. This volume grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo, in 1977. While writing this English version, the author has tried to rearrange and rewrite the original material so that even beginners can read it easily without referring to other books, such as textbooks on commutative algebra. The reader is only expected to know the definition of Noetherin rings and the statement of the Hilbert basis theorem. The new chapters 1, 2, and 10 have been expanded. In particular, the exposition of D-dimension theory, although shorter, is more complete than in the old version. However, to keep the book of manageable size, the latter parts of Chapters 6, 9, and 11 have been removed. I thank Mr. A. Sevenster for encouraging me to write this new version, and Professors K. K. Kubota in Kentucky and P. M. H. Wilson in Cam bridge for their careful and critical reading of the English manuscripts and typescripts. I held seminars based on the material in this book at The University of Tokyo, where a large number of valuable comments and suggestions were given by students Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.

Algebraic Curves and Riemann Surfaces

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821802682
Total Pages : 390 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda

Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book was easy to understand, with many examples. The exercises were well chosen, and served to give further examples and developments of the theory. --William Goldman, University of Maryland In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.

Methods of algebraic geometry

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Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (174 download)

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Book Synopsis Methods of algebraic geometry by : W. V. D. Hodge

Download or read book Methods of algebraic geometry written by W. V. D. Hodge and published by . This book was released on 1954 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: