Schubert Varieties and Degeneracy Loci

• Main Authors: Fulton, William (Author, http://id.loc.gov/vocabulary/relators/aut), Pragacz, Piotr (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Edition: 1st ed. 1998.
• Series: Lecture Notes in Mathematics, 1689
• Subjects: Algebraic geometry.; Combinatorics.; Group theory.; Algebraic topology.; Algebraic Geometry.; Group Theory and Generalizations.; Algebraic Topology.

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 interest...

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.