Overview
- Includes papers written by leading experts in the field
- Contains a selection of articles exploring rationality problems in algebraic geometry
- Gives a representative sample of problems and most recent results in algebraic geometry
- May serve as an intense introduction for graduate students and those wishing to pursue research in algebraic geometry, more specifically, rationality problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 282)
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Table of contents (11 chapters)
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Front Matter
Keywords
About this book
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
Editors and Affiliations
Bibliographic Information
Book Title: Cohomological and Geometric Approaches to Rationality Problems
Book Subtitle: New Perspectives
Editors: Fedor Bogomolov, Yuri Tschinkel
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-0-8176-4934-0
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2010
Hardcover ISBN: 978-0-8176-4933-3Published: 10 December 2009
eBook ISBN: 978-0-8176-4934-0Published: 03 November 2009
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: X, 314
Number of Illustrations: 47 b/w illustrations
Topics: Algebraic Geometry, Group Theory and Generalizations, Topological Groups, Lie Groups