Projective structures on Riemann surface and natural differential\n operators

2019/11/29 by Indranil Biswas, Biswas, Indranil, Sorin Dumitrescu +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1911.13177

openalex publication_date 2019/11/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We investigate the holomorphic differential operators on a Riemann surface\nM. This is done by endowing M with a projective structure. Let mathcal L\nbe a theta characteristic on M. We explicitly describe the jet bundle\nJ^k(E\⊗ mathcal L^{\⊗ n}), where E is a holomorphic vector\nbundle on M equipped with a holomorphic connection, for all k and n. This\nprovides a description of holomorphic differential operators from E\⊗\n mathcal L^{\⊗ n} to another holomorphic vector bundle F using the\nnatural isomorphism \Diff^k(E\⊗ mathcal L^{\⊗ n}, F)=\nF\⊗ (J^k(E\⊗ mathcal L^{\⊗ n}))^*.\n

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