Birationally Rigid Varieties
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Birationally Rigid Varieties
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Author : Aleksandr V. Pukhlikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-05-15
Birationally Rigid Varieties written by Aleksandr V. Pukhlikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-15 with Mathematics categories.
Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the
Birationally Rigid Fano Threefold Hypersurfaces
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Author : Ivan Cheltsov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20
Birationally Rigid Fano Threefold Hypersurfaces written by Ivan Cheltsov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Hypersurfaces categories.
The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.
Birational Geometry K Hler Einstein Metrics And Degenerations
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Author : Ivan Cheltsov
language : en
Publisher: Springer Nature
Release Date : 2023-05-23
Birational Geometry K Hler Einstein Metrics And Degenerations written by Ivan Cheltsov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.
This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.
Cohomological And Geometric Approaches To Rationality Problems
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-03
Cohomological And Geometric Approaches To Rationality Problems written by Fedor Bogomolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-03 with Mathematics categories.
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Automorphisms In Birational And Affine Geometry
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Author : Ivan Cheltsov
language : en
Publisher: Springer
Release Date : 2014-06-11
Automorphisms In Birational And Affine Geometry written by Ivan Cheltsov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
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.
Explicit Birational Geometry Of 3 Folds
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Author : Alessio Corti
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-27
Explicit Birational Geometry Of 3 Folds written by Alessio Corti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-27 with Mathematics categories.
This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.
Surveys In Geometry And Number Theory
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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-18
Surveys In Geometry And Number Theory written by Nicholas Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-18 with Mathematics categories.
A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.
Birational Geometry Of Hypersurfaces
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Author : Andreas Hochenegger
language : en
Publisher: Springer Nature
Release Date : 2019-10-08
Birational Geometry Of Hypersurfaces written by Andreas Hochenegger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
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.
Rationality Of Varieties
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Author : Gavril Farkas
language : en
Publisher: Springer Nature
Release Date : 2021-10-19
Rationality Of Varieties written by Gavril Farkas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Mathematics categories.
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.
Rationality Problems In Algebraic Geometry
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Author : Arnaud Beauville
language : en
Publisher: Springer
Release Date : 2016-12-06
Rationality Problems In Algebraic Geometry written by Arnaud Beauville and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-06 with Mathematics categories.
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.