| Cohomological and Geometric Approaches to Rationality Problems: New Perspectives 2010 Edition Contributor(s): Bogomolov, Fedor (Editor), Tschinkel, Yuri (Editor) |
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ISBN: 0817649336 ISBN-13: 9780817649333 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: December 2009 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Algebra - Abstract - Mathematics | Group Theory |
| Dewey: 516.35 |
| LCCN: 2009939069 |
| Series: Progress in Mathematics |
| Physical Information: 0.75" H x 6.14" W x 9.21" (1.39 lbs) 314 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. B hning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov |