Cohomological and geometric approaches to rationality problems: new perspectives

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 hasled 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" Includespapers written by leading experts in the field Contains a selection of articles exploring rationality problems in algebraic geometry Gives a representativesample of problems and most recent results in algebraic geometry May serve asan intense introduction for graduate students and those wishing to pursue research in algebraic geometry, more specifically, rationality problems INDICE: Preface.- Unremified cohomology of finite groups of Lie type.- Therationality 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.- Generalized homological mirror symmetry and rationality questions.- The Bogomolov multiplier of finite simple groups.- The rationality problem and birational rigidity.

• ISBN: 978-0-8176-4933-3
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 285
• Fecha Publicación: 01/12/2009
• Nº Volúmenes: 1
• Idioma: Inglés