Cohomological and Geometric Approaches to Rationality Problems

New Perspectives

  • Fedor Bogomolov
  • Yuri Tschinkel

Part of the Progress in Mathematics book series (PM, volume 282)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ingrid Bauer, Fabrizio Catanese
    Pages 1-16
  3. Fedor Bogomolov, Tihomir Petrov, Yuri Tschinkel
    Pages 55-73
  4. Ivan Cheltsov, Jihun Park
    Pages 75-132
  5. Shou-Jen Hu, Ming-chang Kang
    Pages 149-162
  6. Boris Kunyavskiĭ
    Pages 209-217
  7. Alexander Kuznetsov
    Pages 219-243
  8. Yuri G Prokhorov
    Pages 245-273
  9. Aleksandr V. Pukhlikov
    Pages 275-311

About this book


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


Bogomolov multiplier Cohomology Noether's Problem algebraic varieties birational rigidity moduli space p-groups

Editors and affiliations

  • Fedor Bogomolov
    • 1
  • Yuri Tschinkel
    • 2
  1. 1.Department of Mathematics, Courant Institute of Math. SciencesNew York UniversityNew YorkUSA
  2. 2.Department of Mathematics, Courant Institute of Math. SciencesNew York UniversityNew YorkUSA

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2010
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4933-3
  • Online ISBN 978-0-8176-4934-0
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book