Duke Mathematical Journal

Grothendieck classes of quiver varieties

Anders Skovsted Buch

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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.

Article information

Source
Duke Math. J. Volume 115, Number 1 (2002), 75-103.

Dates
First available in Project Euclid: 26 May 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1085598119

Digital Object Identifier
doi:10.1215/S0012-7094-02-11513-0

Mathematical Reviews number (MathSciNet)
MR1932326

Zentralblatt MATH identifier
01869849

Subjects
Primary: 14C35: Applications of methods of algebraic $K$-theory [See also 19Exx]
Secondary: 05E10: Combinatorial aspects of representation theory [See also 20C30] 19E08: $K$-theory of schemes [See also 14C35]

Citation

Buch, Anders Skovsted. Grothendieck classes of quiver varieties. Duke Math. J. 115 (2002), no. 1, 75--103. doi:10.1215/S0012-7094-02-11513-0. http://projecteuclid.org/euclid.dmj/1085598119.


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