Criteria for existence of stable parahoric \SO_n, \Sp_n and \Spin bundles on \PP¹

2012/02/09 by Yashonidhi Pandey, Pandey, Yashonidhi · 1 citation
Mathematics · #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14H60

paper · pdf · doi:10.48550/arxiv.1202.1897

34 pages, major revision : shortened, last section added, introduction rewritten

openalex publication_date 2012/02/09 · arxiv created 2013/04/12 · arxiv updated 2013/04/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let p: Y \ra X be a Galois cover of smooth projective curves over \CC with Galois group Γ. This paper is devoted to the study of principal orthogonal and symplectic bundles E on Y to which the action of Γ on Y lifts. We notably describe them intrinsically in terms of objects defined on X and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable (and semi-stable) parahoric special orthogonal, symplectic and spin bundles on the projective line \PP¹.

Citations

• Moduli of parahoric \mathcal G--torsors on a compact Riemann surface

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• Conformal blocks, parahoric torsors and Borel-Weil-Bott

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