Cohomological and Geometric Approaches to Rationality Problems (eBook)
X, 314 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4934-0 (ISBN)
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
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. Bohning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Contents 6
Preface 8
The Rationality of Certain Moduli Spaces of Curves of Genus 3 11
The Rationality of the Moduli Space of Curves of Genus 3 after P. Katsylo 27
Unramified Cohomology of Finite Groups of Lie Type 64
Sextic Double Solids 83
Moduli Stacks of Vector Bundles on Curves and the King- Schofield Rationality Proof 141
Noether's Problem for Some p-Groups 157
Generalized Homological Mirror Symmetry and Rationality Questions 171
The Bogomolov Multiplier of Finite Simple Groups 217
Derived Categories of Cubic Fourfolds 226
Fields of Invariants of Finite Linear Groups 251
The Rationality Problem and Birational Rigidity 280
| Erscheint lt. Verlag | 3.11.2009 |
|---|---|
| Reihe/Serie | Progress in Mathematics | Progress in Mathematics |
| Zusatzinfo | X, 314 p. 47 illus. |
| Verlagsort | Boston |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Technik | |
| Schlagworte | Algebraic Varieties • birational rigidity • Bogomolov multiplier • cohomology • moduli space • Noether's Problem • p-groups |
| ISBN-10 | 0-8176-4934-4 / 0817649344 |
| ISBN-13 | 978-0-8176-4934-0 / 9780817649340 |
| Haben Sie eine Frage zum Produkt? |
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