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arXiv · 2302.09245

A stacky approach to identifying the semistable locus of bundles

Dario Weissmann·Xucheng Zhang
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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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Dario Weissmann, Xucheng Zhang. 2024-03-18. A stacky approach to identifying the semistable locus of bundles. https://doi.org/10.14231/ag-2025-008

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