Grothendieck classes of quiver varieties

Details Grothendieck classes of quiver varieties Grothendieck classes of quiver varieties

2001-04-02

arxiv.org/abs/math/0104029v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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. We furthermore conjecture that the coefficients in our formula have signs which 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 Pragacz.

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