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Frobenius Splitting Methods in Geometry and Representation Theory

  • Michel Brion
  • Shrawan Kumar

Part of the Progress in Mathematics book series (PM, volume 231)

About this book

Introduction

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.

Keywords

Grad algebraic geometry algebraic group commutative alg/ring theory representation theory ring theory

Authors and affiliations

  • Michel Brion
    • 1
  • Shrawan Kumar
    • 2
  1. 1.Institut FourierUniversité Grenoble 1 — CNRSSt.-Martin d’Hères CedexFrance
  2. 2.Department of MathematicsUniversity of North CarolinaChapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b137486
  • Copyright Information Birkhäuser Boston 2005
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4191-7
  • Online ISBN 978-0-8176-4405-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site