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A stacky approach to identifying the semistable locus of bundles

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arxiv 2302.09245 v3 pith:R3VMUPFB submitted 2023-02-18 math.AG

Dario Weissmann , Xucheng Zhang This is my paper · ORCID
classification math.AG
keywords modulibundlesopenadmitslocusmaximalranksemistable
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abstract

We show that the semistable locus is the unique maximal open substack of the moduli stack of principal bundles over a curve that admits a schematic moduli space. For rank $2$ vector bundles it coincides with the unique maximal open substack that admits a separated moduli space, but for higher rank there exist other open substacks that admit separated moduli spaces.

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  1. Rational points in coarse moduli spaces and twisted representations

    math.AG 2025-01 accept novelty 7.0 of 10

    For Schur representations in Azumaya algebras, the coarse moduli space is a quotient algebraic space, and the stack of twisted representations is equivalent to the corresponding quotient stack.

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