On certain Tannakian categories of integrable connections over Kahler manifolds

被引：2

作者：

Biswas, Indranil ^{[1
]}

dos Santos, Joao Pedro ^{[2
]}

Dumitrescu, Sorin ^{[3
]}

Heller, Sebastian ^{[4
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Mumbai 400005, Maharashtra, India

[2] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, 4 Pl Jussieu,Case 247, F-75252 Paris 5, France

[3] Univ Cote dAzur, LJAD, CNRS, Nice, France

[4] Leibniz Univ Hannover, Inst Differentialgeometrie, Welfengarten 1, D-30167 Hannover, Germany

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2022年 / 74卷 / 04期

关键词：

Integrable holomorphic connection; Higgs bundle; neutral Tannakian category; complex torus; Torelli theorem; BUNDLES;

D O I：

10.4153/S0008414X21000201

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a compact Kahler manifold X, it is shown that pairs of the form (E, D), where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on E, produce a neutral Tannakian category. The corresponding pro-algebraic affine group scheme is studied. In particular, it is shown that this pro-algebraic affine group scheme for a compact Riemann surface determines uniquely the isomorphism class of the Riemann surface.

引用

页码：1034 / 1061

页数：28

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