Unfoldings of meromorphic connections and a construction of Frobenius manifolds

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.