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Cohomological and Geometric Approaches to Rationality Problems

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Description

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
Release date Australia
December 10th, 2009
Audience
  • Professional & Vocational
Contributors
  • Edited by Fedor Bogomolov
  • Edited by Yuri Tschinkel
Illustrations
47 Illustrations, black and white; X, 314 p. 47 illus.
Pages
314
Dimensions
156x234x19
ISBN-13
9780817649333
Product ID
3536888

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