Line bundles on the moduli stack of parahoric bundles

Fuente: arXiv
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Main Authors: Damiolini, Chiara, Hong, Jiuzu, Gao, Shuo
Format: Preprint
Published: 2024
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_version_ 1866909803352162304
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