On the L2-Hodge theory of Landau-Ginzburg models.

Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f -twisted Sobolev spaces for the pair (X , f) and prove the corresponding Hodge-to-de Rham degeneration property via L 2 -Hodge theoretical methods when f satisfies an asymptotic condition of strongly ellipticity. This leads to a Frobenius manifold via the Barannikov-Kontsevich construction, unifying the Landau-Ginzburg and Calabi-Yau geometry. Our construction can be viewed as a generalization of K. Saito's higher residue and primitive form theory for isolated singularities. As an application, we construct Frobenius manifolds for orbifold Landau-Ginzburg B-models which admit crepant resolutions. [ABSTRACT FROM AUTHOR]