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＜E-Book＞
Schubert Varieties and Degeneracy Loci / by William Fulton, Piotr Pragacz
(Lecture Notes in Mathematics. ISSN:16179692 ; 1689)

Edition	1st ed. 1998.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1998
Language	English
Size	X, 150 p : online resource
Authors	*Fulton, William author Pragacz, Piotr author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Discrete mathematics LCSH:Group theory LCSH:Algebraic topology FREE:Algebraic Geometry FREE:Discrete Mathematics FREE:Group Theory and Generalizations FREE:Algebraic Topology
Notes	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 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 HTTP:URL=https://doi.org/10.1007/BFb0096380

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