L²-Hodge theoretic construction of Frobenius manifolds for Calabi-Yau smooth projective hypersurfaces

2025/05/24 by Park, Jeehoon, Yoo, Jaewon
#14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.18489

Abstract

We provide a new L²-Hodge theoretic construction of a Frobenius manifold structure on the cohomology of a Calabi-Yau smooth projective hypersurface V, using Li-Wen's L²-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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