Frobenius manifold structures on the spaces of abelian integrals

Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use DD-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 one-dimensional isomonodromic deformations.