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arXiv · 2412.08826

Line bundles on the moduli stack of parahoric bundles

Chiara Damiolini·Jiuzu Hong·Shuo Gao
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Abstract

In this paper we investigate line bundles on $\mathrm{Bun}_{\mathcal{G}}$ the moduli stack of parahoric Bruhat--Tits bundles over a smooth projective curve. Translating this problem into one concerning twisted conformal blocks, we are able to establish criteria that detect when line bundles on an appropriate flag variety descend to $\mathrm{Bun}_{\mathcal{G}}$. Along the way we establish a conjecture of Pappas and Rapoport which describes sections of line bundles on $\mathrm{Bun}_{\mathcal{G}}$ using representation-theoretical means. We conclude the paper with examples where our methods allow us to explicitly determine the Picard group of $\mathrm{Bun}_{\mathcal{G}}$.

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Chiara Damiolini, Jiuzu Hong, Shuo Gao. 2024-12-11. Line bundles on the moduli stack of parahoric bundles. https://arxiv.org/abs/2412.08826

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