Grothendieck classes of quiver varieties
Buch, Anders Skovsted
Algebraic Geometry
Combinatorics
K-Theory and Homology
14M15 (Primary) 14M12, 19E08, 05E05 (Secondary)
Original · EN
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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