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1 October 2002 Grothendieck classes of quiver varieties
Anders Skovsted Buch
Duke Math. J. 115(1): 75-103 (1 October 2002). DOI: 10.1215/S0012-7094-02-11513-0

Abstract

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. Our formula is stated in terms of coefficients that are uniquely determined by the geometry and can be computed by an explicit combinatorial algorithm. We conjecture that these coefficients have signs that alternate with degree. The proof of our formula involves K-theoretic generalizations of several useful cohomological tools, including the Thom-Porteous formula, the Jacobi-Trudi formula, and a Gysin formula of P. Pragacz.

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Anders Skovsted Buch. "Grothendieck classes of quiver varieties." Duke Math. J. 115 (1) 75 - 103, 1 October 2002. https://doi.org/10.1215/S0012-7094-02-11513-0

Information

Published: 1 October 2002
First available in Project Euclid: 26 May 2004

zbMATH: 1052.14056
MathSciNet: MR1932326
Digital Object Identifier: 10.1215/S0012-7094-02-11513-0

Subjects:
Primary: 14C35
Secondary: 05E10 , 19E08

Rights: Copyright © 2002 Duke University Press

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Vol.115 • No. 1 • 1 October 2002
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