Frobenius manifold structures on the spaces of abelian integrals
Differential Geometry
2010-12-30 v2 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that the tangent sheaf multiplication has a cohomological origin, while the Levi-Civita connection is related to 1-dimensional isomonodromic deformations.
Keywords
Cite
@article{arxiv.math/0701581,
title = {Frobenius manifold structures on the spaces of abelian integrals},
author = {Roman M. Fedorov},
journal= {arXiv preprint arXiv:math/0701581},
year = {2010}
}
Comments
Expanded version. The case of an abelian integral with multiple poles is treated. Other minor improvements. Final version