Line bundles on the moduli stack of parahoric bundles
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909803352162304 |
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| author | Damiolini, Chiara Hong, Jiuzu Gao, Shuo |
| author_facet | Damiolini, Chiara Hong, Jiuzu Gao, Shuo |
| contents | 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 $\mathrm{Bun}_{\mathcal{G}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Line bundles on the moduli stack of parahoric bundles Damiolini, Chiara Hong, Jiuzu Gao, Shuo Algebraic Geometry Representation Theory 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 $\mathrm{Bun}_{\mathcal{G}}$. |
| title | Line bundles on the moduli stack of parahoric bundles |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2412.08826 |