# Cohomological and Geometric Approaches to Rationality Problems

## New Perspectives

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

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

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

- DOI https://doi.org/10.1007/978-0-8176-4934-0
- 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