2025/07/08 by Indranil Biswas, Biswas, Indranil, Jacques Hurtubise +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2507.05690
openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal M be a moduli space of stable vector bundles of rank r and determinant ξ on a compact Riemann surface X. Fix a semistable holomorphic vector bundle F on X such that χ(E⊗ F)= 0 for E ∈ \mathcal M. Then any E∈ \mathcal M with H0(X, E⊗ F) = 0 = H1(X, E⊗ F) has a natural holomorphic projective connection. The moduli space of pairs (E, ∇), where E ∈ \mathcal M and ∇ is a holomorphic projective connection on E, is an algebraic T^*\mathcal M--torsor on \mathcal M. We identify this T^*\mathcal M--torsor on \mathcal M with the T^*\mathcal M--torsor given by the sheaf of connections on an ample line bundle over \mathcal M.