Schubert Varieties and Degeneracy Loci / Edition 1

by William Fulton, Piotr Pragacz

Overview

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

Product Details

ISBN-13:	9783540645382
Publisher:	Springer Berlin Heidelberg
Publication date:	08/13/1998
Series:	Lecture Notes in Mathematics , #1689
Edition description:	1998
Pages:	150
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

to degeneracy loci and schubert polynomials.- Modern formulation; Grassmannians, flag varieties, schubert varieties.- Symmetric polynomials useful in geometry.- Polynomials supported on degeneracy loci.- The Euler characteristic of degeneracy loci.- Flag bundles and determinantal formulas for the other classical groups.- and polynomial formulas for other classical groups.- The classes of Brill-Noether loci in Prym varieties.- Applications and open problems.