Comptes Rendus
no. 3
Géométrie algébrique, Géométrie analytique
Moduli space of rank one logarithmic connections over a compact Riemann surface
Anoop Singh1
1 Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Prayagraj 211 019, India
Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 297-301.

Let ℳ 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 ℳ X . We prove that there is a natural compactification of ℳ X and the Picard group of ℳ X is isomorphic to the Picard group of Pic d (X).

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

1 Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Prayagraj 211 019, India
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Anoop Singh},
     title = {Moduli space of rank one logarithmic connections over a compact {Riemann} surface},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {297--301},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.41},
     language = {en},
}
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Anoop Singh. Moduli space of rank one logarithmic connections over a compact Riemann surface. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 297-301. doi : 10.5802/crmath.41. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.41/

[1] Indranil Biswas; Nyshadham Raghavendra 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] Pierre Deligne Équations différentielles á points singuliers réguliers, Lecture Notes in Mathematics, 163, Springer, 1970 | Zbl

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

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

[5] Kyoji Saito 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] Ronnie Sebastian 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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