On the moduli spaces of framed logarithmic connections on a Riemann surface

Indranil Biswas; Michi-aki Inaba; Arata Komyo; Masa-Hiko Saito

doi:10.5802/crmath.199

Analyse et géométrie complexes

On the moduli spaces of framed logarithmic connections on a Riemann surface

Indranil Biswas ¹ ; Michi-aki Inaba ² ; Arata Komyo ³ ; Masa-Hiko Saito ⁴

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
² Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
³ Center for Mathematical and Data Sciences, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan
⁴ Department of Mathematics, Graduate School of Science, Kobe University, Kobe, Rokko, 657-8501, Japan

Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 617-624.

Résumé

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$ -pointed compact Riemann surface.

Reçu le : 2020-12-28
Accepté le : 2021-03-22
Publié le : 2021-07-13

DOI : 10.5802/crmath.199

Classification : 53D30, 14D20, 53B15

Affiliations des auteurs :

Indranil Biswas ¹ ; Michi-aki Inaba ² ; Arata Komyo ³ ; Masa-Hiko Saito ⁴

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2021__359_5_617_0,
     author = {Indranil Biswas and Michi-aki Inaba and Arata Komyo and Masa-Hiko Saito},
     title = {On the moduli spaces of framed logarithmic connections on a {Riemann} surface},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {617--624},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {5},
     year = {2021},
     doi = {10.5802/crmath.199},
     language = {en},
}

TY  - JOUR
AU  - Indranil Biswas
AU  - Michi-aki Inaba
AU  - Arata Komyo
AU  - Masa-Hiko Saito
TI  - On the moduli spaces of framed logarithmic connections on a Riemann surface
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 617
EP  - 624
VL  - 359
IS  - 5
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.199
LA  - en
ID  - CRMATH_2021__359_5_617_0
ER  -

%0 Journal Article
%A Indranil Biswas
%A Michi-aki Inaba
%A Arata Komyo
%A Masa-Hiko Saito
%T On the moduli spaces of framed logarithmic connections on a Riemann surface
%J Comptes Rendus. Mathématique
%D 2021
%P 617-624
%V 359
%N 5
%I Académie des sciences, Paris
%R 10.5802/crmath.199
%G en
%F CRMATH_2021__359_5_617_0

Indranil Biswas; Michi-aki Inaba; Arata Komyo; Masa-Hiko Saito. On the moduli spaces of framed logarithmic connections on a Riemann surface. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 617-624. doi : 10.5802/crmath.199. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.199/

Bibliographie
Cité par

[1] Dima Arinkin Orthogonality of natural sheaves on moduli stacks of $S L (2)$ -bundles with connections on $ℙ^{1}$ minus $4$ points, Sel. Math., New Ser., Volume 7 (2001) no. 2, pp. 213-239 | DOI | MR | Zbl

[2] Michael F. Atiyah Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., Volume 85 (1957), pp. 181-207 | DOI | MR | Zbl

[3] Michael F. Atiyah; Raoul Bott The Yang–Mills equations over Riemann surfaces, Philos. Trans. R. Soc. Lond., Ser. A, Volume 308 (1983), pp. 523-615 | MR | Zbl

[4] Indranil Biswas On the moduli space of holomorphic $G$ -connections on a compact Riemann surface, Eur. J. Math., Volume 6 (2020) no. 2, pp. 321-335 | DOI | MR | Zbl

[5] Indranil Biswas; Viktoria Heu; Jacques Hurtubise Isomonodromic deformations of logarithmic connections and stability, Math. Ann., Volume 366 (2016) no. 1-2, pp. 121-140 | DOI | MR | Zbl

[6] Indranil Biswas; Michi-Aki Inaba; Arata Komyo; Masa-Hiko Saito (in preparation)

[7] Indranil Biswas; Marina Logares; Ana Peón-Nieto Moduli spaces of framed $G$ -Higgs bundles and symplectic geometry, Commun. Math. Phys., Volume 376 (2020) no. 3, pp. 1875-1908 | DOI | MR | Zbl

[8] 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

[9] Ting Chen The associated map of the nonabelian Gauss–Manin connection, Cent. Eur. J. Math., Volume 10 (2012) no. 4, pp. 1407-1421 | DOI | MR | Zbl

[10] William M. Goldman The symplectic nature of fundamental groups of surfaces, Adv. Math., Volume 54 (1984), pp. 200-225 | DOI | MR | Zbl

[11] Michi-Aki Inaba Moduli of parabolic connections on a curve and Riemann–Hilbert correspondence, J. Algebr. Geom., Volume 22 (2013), pp. 407-480 | DOI | MR | Zbl

[12] Michi-Aki Inaba; Katsunori Iwasaki; Masa-Hiko Saito Dynamics of the sixth Painlevé equation, Asymptotic theories and Painlevé equations (Séminaires et Congrès), Volume 14, Société Mathématique de France, 2006, pp. 103-167 | Zbl

[13] Michi-Aki Inaba; Katsunori Iwasaki; Masa-Hiko Saito Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI. I., Publ. Res. Inst. Math. Sci., Volume 42 (2006) no. 4, pp. 987-1089 | DOI | Zbl

[14] Katsunori Iwasaki Fuchsian moduli on a Riemann surface – Its Poisson structure and Poincaré–Lefschetz duality, Pac. J. Math., Volume 155 (1992) no. 2, pp. 319-340 | DOI | Zbl

[15] Michio Jimbo; Tetsuji Miwa; Kimio Ueno Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and $τ$ -function, Physica D, Volume 2 (1981) no. 2, pp. 306-352 | DOI | MR | Zbl

[16] Masa-Hiko Saito; Hitomi Terajima Nodal curves and Riccati solutions of Painlevé equations, J. Math. Kyoto Univ., Volume 44 (2004) no. 3, pp. 529-568 | Zbl

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Einstein–Hermitian connection on twisted Higgs bundles

Indranil Biswas; Tomás L. Gómez; Norbert Hoffmann; ...

C. R. Math (2010)

Stable Higgs bundles on compact Gauduchon manifolds

Indranil Biswas

C. R. Math (2011)

Refinements and Symmetries of the Morris identity for volumes of flow polytopes

Alejandro H. Morales; William Shi

C. R. Math (2021)