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arXiv · 2504.19098

A Construction of Formal Frobenius Manifold from Deformation of Complex Structure

Jian Han
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Abstract

This thesis studies Frobenius manifolds arising from extended deformations of complex structures on compact Calabi-Yau manifolds, following the construction by Sergey Barannikov and Maxim Kontsevich. The work is based on the investigation of formal moduli spaces of solutions to the Maurer-Cartan equations modulo gauge equivalence. We provide a foundational overview of deformation theory from the perspective of differential geometry and prove the equivalence between gauge-equivalent deformations and isomorphic deformations. Based on this framework, we construct a differential Gerstenhaber-Batalin-Vilkovisky (dGBV) algebra associated to the deformation of Calabi-Yau manifolds and then construct the corresponding Frobenius manifold.

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Jian Han. 2025-04-27. A Construction of Formal Frobenius Manifold from Deformation of Complex Structure. https://arxiv.org/abs/2504.19098

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