Biswas, IndranilMuñoz, VicenteBiswas, IndranilKulkarni , Ravi S.Mitra , Sudeb2023-06-202023-06-202010M. F. Atiyah, Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc. 85 (1957), 181-207. I. Biswas and V. Muñoz, Torelli theorem for the moduli spaces of connections on a Riemann surface. Preprint. I. Biswas and N. Raghavendra, Line bundles over a moduli space of logarithmic connections on a Riemann surface.Geom. Funct. Anal. 15 (2005), 780-808. J. Carlson, Extensions of mixed Hodge structures, in: Journees de geometrie algebrique d'Angers Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den Rijn-Germantown, Md., 1980, pp. 107-127. P. Deligne, Equations Differentielles µa Points Singuliers Reguliers. Lecture Notes in Math.163, Springer-Verlag,Berlin, 1970. P. Deligne, Theorie de Hodge, II. Inst. Hautes Etudes Sci. Publ. Math. 40 (1971), 5-57. P. Deligne, Theorie de Hodge, III. Inst. Hautes Etudes Sci. Publ. Math. 44 (1974), 5-77. H. Esnault and E. Viehweg, Logarithmic de Rham complex and vanishing theorems. Invent.Math. 86 (1986), 161-194. P. A. Griffiths and J. Harris, Principles of algebraic geometry. Wiley Classics Library. John Wiley & Sons, Inc., New York, 1994. M. Maruyama, Openness of a family of torsion free sheaves. Jour. Math. Kyoto Univ. 16 (1976), 627-637. N. Nitsure, Moduli of semistable logarithmic connections. Jour. Amer. Math. Soc. 6 (1993),597-609. C. T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I. Inst. Hautes Etudes Sci. Publ. Math. 79 (1994), 47-129. C. T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. II. Inst. Hautes Etudes Sci. Publ. Math. 80 (1994), 5-79. A. Weil, Generalisation des fonctions abeliennes. Jour.Math. Pures Appl. 17 (1938), 47-87.978-1-57146-195-7https://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