There are no exotic compact moduli of sheaves on a curve

Andres Fernandez Herrero; Dario Weissmann; Xucheng Zhang

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arXiv · 2504.11155

There are no exotic compact moduli of sheaves on a curve

Andres Fernandez Herrero·Dario Weissmann·Xucheng Zhang

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Abstract

We study moduli of coherent sheaves of some given degree and positive rank on a curve. We show that there is only one nonempty open condition on families of sheaves that yields a universally closed adequate moduli space, namely, the one that recovers the classical moduli of slope semistable vector bundles.

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Andres Fernandez Herrero, Dario Weissmann, Xucheng Zhang. 2025-04-15. There are no exotic compact moduli of sheaves on a curve. https://arxiv.org/abs/2504.11155

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