Biswas, IndranilMuñoz, VicenteBiswas, IndranilKulkarni , Ravi S.Mitra , Sudeb2023-06-202023-06-202010978-1-57146-195-7https://hdl.handle.net/20.500.14352/45436Proceedings of the U.S.-India workshop in Teichmüller theory and moduli problems,Harish-Chandra Research Institute, Allahabad, January 2006Let E be a holomorphic vector bundle over a compact connected Riemann surface X. The vector bundle E admits a holomorphic projective connection if and only if for every holomorphic direct summand F of E of positive rank, the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix a point x0 in X. There is a logarithmic connection on E, singular over x0 with residue ¡d n IdEx0 if and only if the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix an integer n ¸ 2, and also ¯x an integer d coprime to n. Let M(n; d) denote the moduli space of logarithmic SL(n;C){connections on X singular of x0 with residue ¡ d n Id. The isomorphism class of the variety M(n; d) determines the isomorphism class of the Riemann surface X.engbook parthttp://intlpress.com/site/pub/pages/books/items/00000305/index.htmlhttp://www.mat.ucm.es/~vmunozve/Moduli.pdfopen access512.7Geometria algebraica1201.01 Geometría Algebraica