Frobenius manifold structures on the spaces of abelian integrals

Details Frobenius manifold structures on the spaces of abelian integrals Frobenius manifold structures on the spaces of abelian integrals

2007-01-21

arxiv.org/abs/math/0701581v2

Journal of Geometry and Physics, Vol. 61 (2011), no. 2, pp. 485-497

Mathematics

Differential Geometry

Expanded version. The case of an abelian integral with multiple poles is treated. Other minor improvements. Final version

Scientific paper

10.1016/j.geomphys.2010.10.015

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.

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