Explicit Birational Geometry Of 3 Folds
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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.
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.
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.
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 Mathematics categories.
The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.
Complex Algebraic Threefolds
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Author : Masayuki Kawakita
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-19
Complex Algebraic Threefolds written by Masayuki Kawakita 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 2023-10-19 with Mathematics categories.
A detailed treatment of the explicit aspects of the birational geometry of algebraic threefolds arising from the minimal model program.
Birational Geometry Rational Curves And Arithmetic
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-17
Birational Geometry Rational Curves And Arithmetic 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 2013-05-17 with Mathematics categories.
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.
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.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Fifth International Congress Of Chinese Mathematicians
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Fifth International Congress Of Chinese Mathematicians written by Lizhen Ji 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 2012 with Mathematics categories.
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Surveys On Recent Developments In Algebraic Geometry
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Author : Izzet Coskun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-12
Surveys On Recent Developments In Algebraic Geometry written by Izzet Coskun 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 2017-07-12 with Mathematics categories.
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.