PROJECTIVE STRUCTURE ON RIEMANN SURFACE AND NATURAL DIFFERENTIAL OPERATORS

Indranil Biswas (1) , Sorin Dumitrescu (2)

1 TIFR - Tata Institute for Fundamental Research
2 LJAD - Laboratoire Jean Alexandre Dieudonné

We investigate the holomorphic differential operators on a Riemann surface M. This is done by endowing M with a projective structure. Let L be a theta characteristic on M. We explicitly describe the jet bundle J k (E ⊗ L ⊗n), where E is a holomorphic vector bundle on M equipped with a holomorphic connection, for all k and n. This provides a description of holomorphic differential operators from E ⊗ L ⊗n to another holomorphic vector bundle F using the natural isomorphism Diff k (E ⊗ L ⊗n , F) = F ⊗ (J k (E ⊗ L ⊗n)) * .

Domaines: Mathématiques [math]

Indranil Biswas, Sorin Dumitrescu. PROJECTIVE STRUCTURE ON RIEMANN SURFACE AND NATURAL DIFFERENTIAL OPERATORS. Differential Geometry and its Applications, 2020, 72. ⟨hal-02387407⟩