Frobenius manifold structures on the spaces of abelian integrals
arXiv:math/0701581 · doi:10.1016/j.geomphys.2010.10.015
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.
Expanded version. The case of an abelian integral with multiple poles is treated. Other minor improvements. Final version