Line bundles on the moduli stack of parahoric bundles

2024/12/11 by Chiara Damiolini, Damiolini, Chiara, Jiuzu Hong +2 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.08826

openalex publication_date 2024/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate line bundles on Bun_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 Bun_G. Along the way we establish a conjecture of Pappas and Rapoport which describes sections of line bundles on Bun_G using representation-theoretical means. We conclude the paper with examples where our methods allow us to explicitly determine the Picard group of Bun_G.

Cited by

• Conformal blocks, parahoric torsors and Borel-Weil-Bott
• Level structures on parahoric torsors and complete integrability

Related

• The line bundles on the stack of parabolic G-bundles over curves and their sections
• Some questions about \mathcal G-bundles on curves
• The moduli stack of G-bundles
• Conformal blocks, parahoric torsors and Borel-Weil-Bott
• Uniformization of G-bundles