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Progress in Mathematics #282: Cohomological and Geometric Approaches to Rationality Problems: New Perspectives

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Progress in Mathematics #282: Cohomological and Geometric Approaches to Rationality Problems: New Perspectives Cover

 

Synopses & Reviews

Publisher Comments:

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

Synopsis:

This volume provides an overview of rationality problems by surveying research from leading experts in the field. Readers will find coverage of rationality problems from both cohomological and algebraic geometry perspectives.

Synopsis:

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

Table of Contents

Preface.- Unremified cohomology of finite groups of Lie type.- The rationality of the moduli space of curves of genus 3 after P. Katsylo.- The rationality of certain moduli spaces of curves of genus 3.- on sextic double solids.- moduli stacks of vector bundles on curves and the King--Schofield rationality proof.- Noether's problem for some p-groups.-generalitzed homological mirror symmetry and rationality questions.- The Bogomolov multiplier of finite simple groups.- The rationality problem and birational rigidity.

Product Details

ISBN:
9780817649333
Author:
Bogomolov, Fedor (edt)
Publisher:
Birkhauser
Editor:
Bogomolov, Fedor
Editor:
Tschinkel, Yuri
Author:
Bogomolov, Fedor
Author:
Tschinkel, Yuri
Subject:
Geometry - Algebraic
Subject:
Algebra - Abstract
Subject:
Group Theory
Subject:
Mathematics-Algebraic Geometry
Subject:
Bogomolov multiplier
Subject:
Noether s Problem
Subject:
birational rigidity
Subject:
p-groups
Subject:
Algebraic Geometry
Subject:
Topological Groups, Lie Groups
Subject:
Group Theory and Generalizations
Copyright:
Edition Description:
2010
Series:
Progress in Mathematics
Series Volume:
282
Publication Date:
20091210
Binding:
HARDCOVER
Language:
English
Pages:
324
Dimensions:
235 x 155 mm 1390 gr

Related Subjects


Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory

Progress in Mathematics #282: Cohomological and Geometric Approaches to Rationality Problems: New Perspectives New Hardcover
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$179.00 In Stock
Product details 324 pages Birkhauser Boston - English 9780817649333 Reviews:
"Synopsis" by , This volume provides an overview of rationality problems by surveying research from leading experts in the field. Readers will find coverage of rationality problems from both cohomological and algebraic geometry perspectives.
"Synopsis" by , 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
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