Géométrie algébrique, Géométrie analytique
Moduli space of rank one logarithmic connections over a compact Riemann surface
Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 297-301.

Let X denote the moduli space of rank one logarithmic connections singular over a finite subset S of a compact Riemann surface X with fixed residues. We study the rational functions into X . We prove that there is a natural compactification of X and the Picard group of X is isomorphic to the Picard group of Pic d (X).

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DOI : 10.5802/crmath.41
Classification : 14D20, 14C22, 14E05
Singh, Anoop 1

1 Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Prayagraj 211 019, India
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Singh, Anoop. Moduli space of rank one logarithmic connections over a compact Riemann surface. Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 297-301. doi : 10.5802/crmath.41. http://www.numdam.org/articles/10.5802/crmath.41/

[1] Biswas, Indranil; Raghavendra, Nyshadham Line bundles over a moduli space of logarithmic connections on a Riemann surface, Geom. Funct. Anal., Volume 15 (2005) no. 4, pp. 780-808 | DOI | MR | Zbl

[2] Deligne, Pierre Équations différentielles á points singuliers réguliers, Lecture Notes in Mathematics, 163, Springer, 1970 | Zbl

[3] Lange, Herbert; Birkenhake, Christina Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften, 302, Springer, 1992 | MR | Zbl

[4] Nitsure, Nitin Moduli of semistable logarithmic connections, J. Am. Math. Soc., Volume 6 (1993) no. 3, pp. 597-609 | DOI | MR | Zbl

[5] Saito, Kyoji Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci., Univ. Tokyo, Sect. I A, Volume 27 (1980) no. 2, pp. 265-291 | MR | Zbl

[6] Sebastian, Ronnie Torelli theorems for moduli of logarithmic connections and parabolic bundles, Manuscr. Math., Volume 136 (2011) no. 1-2, pp. 249-271 | DOI | MR | Zbl

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