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TOWARDS AN INTERSECTION CHOW COHOMOLOGY THEORY FOR GIT QUOTIENTS

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Abstract

We study the Fulton-MacPherson operational Chow rings of good moduli spaces of properly stable, smooth, Artin stacks. Such spaces are étale locally isomorphic to geometric invariant theory quotients of affine schemes, and are therefore natural extensions of GIT quotients. Our main result is that, with ℚ-coefficients, every operational class can be represented by a topologically strong cycle on the corresponding stack. Moreover, this cycle is unique modulo rational equivalence on the stack. Our methods also allow us to prove that if X is the good moduli space of a properly stable, smooth, Artin stack then the natural map Pic(X)ℚ, L ↦ c1(L) is an isomorphism.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    DAN EDIDIN

  2. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    MATTHEW SATRIANO

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  1. DAN EDIDIN
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  2. MATTHEW SATRIANO
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Correspondence to DAN EDIDIN.

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Dan Edidin Supported by Simons Collaboration Grant 315460.

Matthew Satriano Supported by a Discovery Grant from the National Science and Engineering Board of Canada.

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EDIDIN, D., SATRIANO, M. TOWARDS AN INTERSECTION CHOW COHOMOLOGY THEORY FOR GIT QUOTIENTS. Transformation Groups 25, 1103–1124 (2020). https://doi.org/10.1007/s00031-020-09553-9

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