English

On certain Tannakian categories of integrable connections over Kaehler manifolds

Algebraic Geometry 2021-04-13 v2 Differential Geometry

Abstract

Given a compact Kaehler 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 EE, 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.

Keywords

Cite

@article{arxiv.2008.11483,
  title  = {On certain Tannakian categories of integrable connections over Kaehler manifolds},
  author = {Indranil Biswas and João Pedro dos Santos and Sorin Dumitrescu and Sebastian Heller},
  journal= {arXiv preprint arXiv:2008.11483},
  year   = {2021}
}

Comments

Final version; to appear in Canadian Journal of Mathematics