Torsors on moduli spaces of principal G-bundles

2024/04/19 by Indranil Biswas, Biswas, Indranil, Swarnava Mukhopadhyay +1
Mathematics · #14D20 #14D21 #14H60 #17B67 #32G34 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2404.12877

openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a semisimple complex algebraic group with a simple Lie algebra \mathfrakg, and let M⁰_G denote the moduli stack of topologically trivial stable G-bundles on a smooth projective curve C. Fix a theta characteristic κ on C which is even in case dim\mathfrakg is odd. We show that there is a nonempty Zariski open substack \mathcal U_κ of M⁰_G such that Hⁱ(C, ad(E_G)⊗κ) = 0, i = 1, 2, for all E_G ∈ \mathcal U_κ. It is shown that any such E_G has a canonical connection. It is also shown that the tangent bundle TU_κ has a natural splitting, where U_κ is the restriction of U_κ to the semi-stable locus. We also produce an isomorphism between two naturally occurring Ω¹_M^rs_G--torsors on the moduli space of regularly stable M^rs_G.

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