Flat meromorphic connections of Frobenius manifolds with tt*-structure
Differential Geometry
2011-10-11 v1 Algebraic Geometry
Abstract
The base space of a semi-universal unfolding of a hypersurface singularity carries a rich geometric structure, which was axiomatized as a CDV-structure by C. Hertling. For any CDV-structure on a Frobenius manifold M, the pull-back of the (1,0)-tangent bundle of M to the product of M by the complex line carries two natural holomorphic structures equipped with flat meromorphic connections. We show that, for any semi-simple CDV-structure, there is a formal isomorphism between these two bundles compatible with connections. Moreover, if we assume that the super-symmetric index Q vanishes, we give a necessary and sufficient condition for such a formal isomorphism to be convergent, and we make it explicit for dim M = 2.
Keywords
Cite
@article{arxiv.1105.1542,
title = {Flat meromorphic connections of Frobenius manifolds with tt*-structure},
author = {Jiezhu Lin and Claude Sabbah},
journal= {arXiv preprint arXiv:1105.1542},
year = {2011}
}