$L^2$-Hodge theoretic construction of Frobenius manifolds for Calabi-Yau smooth projective hypersurfaces

Jeehoon Park; Jaewon Yoo

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arXiv · 2505.18489

$L^2$-Hodge theoretic construction of Frobenius manifolds for Calabi-Yau smooth projective hypersurfaces

Jeehoon Park·Jaewon Yoo

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Abstract

We provide a new $L^2$-Hodge theoretic construction of a Frobenius manifold structure on the cohomology of a Calabi-Yau smooth projective hypersurface $V$, using Li-Wen's $L^2$-Hodge theory [9] of a Landau-Ginzburg model with compact critical locus $V$. We also give a precise comparison result between the current construction and Barannikov-Kontsevich's construction [2] of the Frobenius manifold structure on the cohomology of $V$.

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Jeehoon Park, Jaewon Yoo. 2025-05-24. $L^2$-Hodge theoretic construction of Frobenius manifolds for Calabi-Yau smooth projective hypersurfaces. https://arxiv.org/abs/2505.18489

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