Overview

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

Full Product Details

Author:   Fedor Bogomolov ,  Yuri Tschinkel
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2010 ed.
Volume:   282
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   1.390kg
ISBN:  

9780817649333

ISBN 10:   0817649336
Pages:   314
Publication Date:   10 December 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

The Rationality of Certain Moduli Spaces of Curves of Genus 3.- The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo.- Unramified Cohomology of Finite Groups of Lie Type.- Sextic Double Solids.- Moduli Stacks of Vector Bundles on Curves and the King#x2013;Schofield Rationality Proof.- Noether#x2019;s Problem for Some -Groups.- Generalized Homological Mirror Symmetry and Rationality Questions.- The Bogomolov Multiplier of Finite Simple Groups.- Derived Categories of Cubic Fourfolds.- Fields of Invariants of Finite Linear Groups.- The Rationality Problem and Birational Rigidity.

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