English

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

R2 v1 2026-07-22T17:49:40.198Z