Unfoldings of meromorphic connections and a construction of Frobenius manifolds

2002/07/10 by Claus Hertling, Yuri I. Manin, Hertling, Claus +2
Mathematics · #32G20 #32G34 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:32G20 #msc:32G34

paper · pdf · doi:10.48550/arxiv.math/0207089

34 pages, amslatex, remark 2.10 added, shorter proof of 2.9

openalex publication_date 2002/07/10 · arxiv created 2003/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence of universal unfoldings of certain germs of meromorphic connections is established. This is used to prove a general construction theorem for Frobenius manifolds. A particular case is Dubrovin's theorem on semisimple Frobenius manifolds. Another special case starts with variations of Hodge structures. This case is used to compare two constructions of Frobenius manifolds, the one in singularity theory and the Barannikov-Kontsevich construction. For homogeneous polynomials which give Calabi-Yau hypersurfaces certain Frobenius submanifolds in both constructions are isomorphic.

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