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arXiv · 2408.10551

Schwartz $κ$-densities on the moduli stack of rank $2$ bundles near stable bundles

David Kazhdan·Alexander Polishchuk
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Abstract

Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of stable bundles of rank $2$ and fixed odd degree determinant over $C$, coming from the Schwartz space of $κ$-densities on the corresponding stack of bundles (earlier we proved that these functions are locally constant on the locus of very stable bundles). We prove the relevant algebro-geometric statements for curves of genus $2$ and for non-hyperelliptic curves of genus $3$.

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David Kazhdan, Alexander Polishchuk. 2025-02-27. Schwartz $κ$-densities on the moduli stack of rank $2$ bundles near stable bundles. https://arxiv.org/abs/2408.10551

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