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Chern class formulas for quiver varieties

Anders S. Buch·William Fulton
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Abstract

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on arbitrary composites of the maps. Our answer is a polynomial in Chern classes of the bundles involved, depending on the given rank conditions. It can be expressed as a linear combination of products of Schur polynomials in the differences of the bundles. The coefficients are interesting generalizations of Littlewood-Richardson numbers. These polynomials specialize to give new formulas for Schubert polynomials.

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BibTeXRIS

Anders S. Buch, William Fulton. 1998-04-07. Chern class formulas for quiver varieties. https://doi.org/10.1007/s002220050297

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