Birational Geometry Of Algebraic Varieties

Author : Janos Kollár,Shigefumi Mori
Publisher : Cambridge University Press
Page : 264 pages
File Size : 43,9 Mb
Release : 2008-02-04
Category : Mathematics
ISBN : 0521060222

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Birational Geometry of Algebraic Varieties by Janos Kollár,Shigefumi Mori Pdf

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.

Author : S. Iitaka
Publisher : Springer
Page : 357 pages
File Size : 41,6 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 1461381215

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Algebraic Geometry by S. Iitaka Pdf

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.

Author : Shigeru Iitaka
Publisher : Unknown
Page : 357 pages
File Size : 49,9 Mb
Release : 1982
Category : Algebraic varieties
ISBN : 3540905464

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Algebraic Geometry by Shigeru Iitaka Pdf

Author : Anonim
Publisher : Unknown
Page : 65 pages
File Size : 44,6 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:630444176

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Birational Geometry of Algebraic Varieties by Anonim Pdf

Author : Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini
Publisher : Springer Nature
Page : 200 pages
File Size : 44,6 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030371142

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Birational Geometry and Moduli Spaces by Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini Pdf

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.

Author : Janos Kollár,Shigefumi Mori
Publisher : Cambridge University Press
Page : 264 pages
File Size : 49,7 Mb
Release : 1998-09-17
Category : Mathematics
ISBN : 9780521632775

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Birational Geometry of Algebraic Varieties by Janos Kollár,Shigefumi Mori Pdf

This book provides the first comprehensive introduction to the circle of ideas developed around Mori's program.

Author : S. Iitaka
Publisher : Springer
Page : 376 pages
File Size : 42,7 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:49015000693433

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Algebraic Geometry by S. Iitaka Pdf

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.

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,6 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9781461464822

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Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

​​​​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.

Author : Janos Kollár,Shigefumi Mori
Publisher : Cambridge University Press
Page : 254 pages
File Size : 42,9 Mb
Release : 2010-03-24
Category : Mathematics
ISBN : 0511662564

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Birational Geometry of Algebraic Varieties by Janos Kollár,Shigefumi Mori Pdf

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.

Author : V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 49,9 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9780821872888

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Algebraic Groups and Their Birational Invariants by V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski Pdf

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.

Author : V.I. Danilov,V.V. Shokurov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 45,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578786

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Algebraic Geometry I by V.I. Danilov,V.V. Shokurov Pdf

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Author : Ivan Cheltsov,Ciro Ciliberto,Hubert Flenner,James McKernan,Yuri G. Prokhorov,Mikhail Zaidenberg
Publisher : Springer
Page : 509 pages
File Size : 44,6 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9783319056814

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Automorphisms in Birational and Affine Geometry by Ivan Cheltsov,Ciro Ciliberto,Hubert Flenner,James McKernan,Yuri G. Prokhorov,Mikhail Zaidenberg Pdf

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.

Author : Janos Kollar
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 43,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662032763

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Rational Curves on Algebraic Varieties by Janos Kollar Pdf

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.

Author : Thomas Peternell,Joichi Miyaoka
Publisher : Birkhäuser
Page : 221 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888936

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Geometry of Higher Dimensional Algebraic Varieties by Thomas Peternell,Joichi Miyaoka Pdf

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.

Author : Ciro Ciliberto
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 43,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851791

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Classification of Algebraic Varieties by Ciro Ciliberto Pdf

This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of algebraic varieties, toric varieties. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of areas of current research.