Ebook: Cohomological and Geometric Approaches to Rationality Problems: New Perspectives
- Tags: Algebraic Geometry, Topological Groups Lie Groups, Group Theory and Generalizations
- Series: Progress in Mathematics 282
- Year: 2010
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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
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. B?hning
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
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. B?hning
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
Content:
Front Matter....Pages i-ix
The Rationality of Certain Moduli Spaces of Curves of Genus 3....Pages 1-16
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo....Pages 17-53
Unramified Cohomology of Finite Groups of Lie Type....Pages 55-73
Sextic Double Solids....Pages 75-132
Moduli Stacks of Vector Bundles on Curves and the King–Schofield Rationality Proof....Pages 133-148
Noether’s Problem for Some p-Groups....Pages 149-162
Generalized Homological Mirror Symmetry and Rationality Questions....Pages 163-208
The Bogomolov Multiplier of Finite Simple Groups....Pages 209-217
Derived Categories of Cubic Fourfolds....Pages 219-243
Fields of Invariants of Finite Linear Groups....Pages 245-273
The Rationality Problem and Birational Rigidity....Pages 275-311
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. B?hning
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
Content:
Front Matter....Pages i-ix
The Rationality of Certain Moduli Spaces of Curves of Genus 3....Pages 1-16
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo....Pages 17-53
Unramified Cohomology of Finite Groups of Lie Type....Pages 55-73
Sextic Double Solids....Pages 75-132
Moduli Stacks of Vector Bundles on Curves and the King–Schofield Rationality Proof....Pages 133-148
Noether’s Problem for Some p-Groups....Pages 149-162
Generalized Homological Mirror Symmetry and Rationality Questions....Pages 163-208
The Bogomolov Multiplier of Finite Simple Groups....Pages 209-217
Derived Categories of Cubic Fourfolds....Pages 219-243
Fields of Invariants of Finite Linear Groups....Pages 245-273
The Rationality Problem and Birational Rigidity....Pages 275-311
....