Frobenius Splitting Methods in Geometry and Representation Theory

Frobenius Splitting: General Theory.- Frobenius Splitting of Schubert Varieties.- Cohomology and Geometry of Schubert Varieties.- Canonical Splitting and Good Filtration.- Cotangent Bundles of Flag Varieties.- Equivariant Embeddings of Reductive Groups.- Hilbert Schemes of Points on Surfaces.

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)

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.