Schubert Varieties and Degeneracy Loci

1998
ISBN: 978-3-540-64538-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1689, 150 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 254 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Pragacz, Piotr

Fulton, William

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.