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arxiv: math/0104029 · v1 · submitted 2001-04-02 · 🧮 math.AG · math.CO· math.KT

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Grothendieck classes of quiver varieties

Anders Skovsted Buch
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classification 🧮 math.AG math.COmath.KT
keywords formulagrothendieckquivervarietyalternateclassescoefficientscohomological
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

    hep-th 2026-01 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for partial flag manifolds reproduce parabolic Whitney polynomials for Schubert classes in quantum K-theory and yield new parabolic quantum Grothendieck polynomials.

  2. Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

    hep-th 2025-12 unverdicted novelty 7.0

    Schubert line defects in 3d GLSMs for complete flag manifolds are realized as SQM quivers whose indices give quantum Grothendieck polynomials and restrict the target space to Schubert varieties.