Overview
- Applies Frobenius splitting methods to algebraic geometry and various problems in representation theory
- Unique in book literature, systematically develops the theory and covers all its major developments
- Will be an excellent resource for mathematicians and graduate students in algebraic geometry and representation theory of algebraic groups
Part of the book series: Progress in Mathematics (PM, volume 231)
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Table of contents (7 chapters)
Keywords
About this book
The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and representation theory. This work, unique in book literature, systematically develops the theory and covers all its major developments.
Key features:
* Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research
* Studies in detail the geometry of Schubert varieties, their syzygies, equivariant embeddings of reductive groups, Hilbert Schemes, canonical splittings, good filtrations, among other topics
* Applies Frobenius splitting methods to algebraic geometry and various problems in representation theory
* Many examples, exercises, and open problems suggested throughout
* Comprehensive bibliography and index
This book will be an excellent resource for mathematicians and graduate students in algebraic geometry and representation theory of algebraic groups.
Reviews
From the reviews:
"The present momgraphy is the first exposition in book form of this theory and of its major applications. Each section of the book is complemented with exerices; each chapter ends with useful comments, and open problems are suggested throughout. The book leads clearly and rapidly an interested reader from basic results to the research level." ---Zentralblatt MATH
"The book is an excellent source for getting familiar with the recent developments in geometric and representation theoretic questions in the theory of algebraic groups, mainly in characteristic p." ---Monatshefte für Mathematik
“This is a truly fantastic book. It is the first comprehensive text on Frobenius splitting and its applications to geometry and representation theory. If this was a one-paragraph review, I would say buy the book, study it carefully and then apply the contents to a research project’. The readers (and the reviewer) are in the authors’debt.”(MATHEMATICAL REVIEWS)
Authors and Affiliations
Bibliographic Information
Book Title: Frobenius Splitting Methods in Geometry and Representation Theory
Authors: Michel Brion, Shrawan Kumar
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/b137486
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2005
Hardcover ISBN: 978-0-8176-4191-7Published: 10 December 2004
eBook ISBN: 978-0-8176-4405-5Published: 08 August 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: X, 250
Topics: Algebraic Geometry, Group Theory and Generalizations