Schubert Varieties and Degeneracy Loci. Lecture Notes in Mathematics Vol.1689

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.

Preface.- Introduction 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 manifolds and determinantal formulas for other classical groups.- P-and Q-polynomial formulas for other classical groups.- The classes of Brill-Noether loci in Prym varieties.- Applications and open problems.- Appendices.

William Fulton Piotr Pragacz 

Mathematik Algebra Arithmetik Mathematik/Arithmetik/Algebra 

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