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Cohomological and Geometric Approaches to Rationality Problems: New Perspectives (Progress in Mathematics Book 282) 🔍
Ingrid Bauer, Fabrizio Catanese (auth.), Fedor Bogomolov, Yuri Tschinkel (eds.) Birkhäuser Boston : Imprint: Birkhäuser, Progress in Mathematics, Progress in Mathematics 282, 1, 2010
英语 [en] · PDF · 3.1MB · 2010 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
Rationality problems link algebra to geometry. The difficulties involved depend on the transcendence degree over the ground field, 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. These advances have led to many interdisciplinary applications of algebraic geometry.
This comprehensive text consists of surveys and research papers by leading specialists in the field. Topics discussed include the rationality of quotient spaces, cohomological invariants of finite groups of Lie type, rationality of moduli spaces of curves, and rational points on algebraic varieties.
This volume is intended for research mathematicians and graduate students interested in algebraic geometry, and specifically in rationality problems.
I. Bauer
C. Böhning
F. Bogomolov
F. Catanese
I. Cheltsov
N. Hoffmann
S.-J. Hu
M.-C. Kang
L. Katzarkov
B. Kunyavskii
A. Kuznetsov
J. Park
T. Petrov
Yu. G. Prokhorov
A.V. Pukhlikov
Yu. Tschinkel
备用文件名
lgrsnf/A:\compressed\10.1007%2F978-0-8176-4934-0.pdf
备用文件名
nexusstc/Cohomological and Geometric Approaches to Rationality Problems: New Perspectives/06040178e61f60fb2bb37e0543092f01.pdf
备用文件名
scihub/10.1007/978-0-8176-4934-0.pdf
备用文件名
zlib/Science (General)/Ingrid Bauer, Fabrizio Catanese (auth.), Fedor Bogomolov, Yuri Tschinkel (eds.)/Cohomological and Geometric Approaches to Rationality Problems: New Perspectives_2129973.pdf
备选作者
Fedor Bogomolov, Yuri Tschinkel, editors
备选作者
Bogomolov, Fedor; Tschinkel, Yuri
备选作者
Joseph Varon; Pilar Acosta
备用出版商
Birkhäuser Basel
备用出版商
Scholars Portal
备用出版商
Springer
备用版本
Progress in mathematics -- v. 282, Progress in mathematics (Boston, Mass.) -- v. 282., Boston, Massachusetts, 2010
备用版本
Progress in mathematics (Boston, Mass.), vol. 282, Boston, cop. 2010
备用版本
Progress in Mathematics, 282, 1st ed. 2010, Boston, MA, 2010
备用版本
Progress in Mathematics, 282, v. v. 282, 1, Boston, 2010
备用版本
United States, United States of America
备用版本
Springer Nature, Boston, 2010
备用版本
Progress in Mathematics, 2009
备用版本
Apr 29, 2010
备用版本
2010, 2009
元数据中的注释
lg976050
元数据中的注释
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元数据中的注释
Includes bibliographical references.
备用描述
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
备用描述
Front Matter....Pages i-ix
The Rationality of Certain Moduli Spaces of Curves of Genus 3....Pages 1-16
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo....Pages 17-53
Unramified Cohomology of Finite Groups of Lie Type....Pages 55-73
Sextic Double Solids....Pages 75-132
Moduli Stacks of Vector Bundles on Curves and the King–Schofield Rationality Proof....Pages 133-148
Noether’s Problem for Some p -Groups....Pages 149-162
Generalized Homological Mirror Symmetry and Rationality Questions....Pages 163-208
The Bogomolov Multiplier of Finite Simple Groups....Pages 209-217
Derived Categories of Cubic Fourfolds....Pages 219-243
Fields of Invariants of Finite Linear Groups....Pages 245-273
The Rationality Problem and Birational Rigidity....Pages 275-311
备用描述
This Comprehensive Text Consists Of Surveys And Research Papers By Leading Specialists In The Field. Topics Discussed Include The Rationality Of Quotient Spaces, Cohomological Invariants Of Finite Groups Of Lie Type, Rationality Of Moduli Spaces Of Curves, And Rational Points On Algebraic Varieties. This Volume Is Intended For Research Mathematicians And Graduate Students Interested In Algebraic Geometry, And Specifically In Rationality Problems.--jacket. Fedor Bogomolov, Yuri Tschinkel, Editors. Includes Bibliographical References.
备用描述
Progress in Mathematics
Erscheinungsdatum: 10.12.2009
开源日期
2013-08-01
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