A construction of Frobenius manifolds with logarithmic poles and applications

TL;DR

This paper develops a new method for constructing Frobenius manifolds with logarithmic poles, extending previous theorems and applying to Gromov-Witten theory and Hodge structures.

Contribution

It generalizes Hertling and Manin's theorem and introduces a new construction approach for Frobenius manifolds with applications in algebraic geometry.

Findings

Generalized reconstruction theorem for Gromov-Witten invariants

Constructed Frobenius manifolds from degenerating Hodge structures

Extended the class of Frobenius manifolds with logarithmic poles

Abstract

A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and Manin for projective smooth varieties with convergent Gromov-Witten potential. A second application is a construction of Frobenius manifolds out of a variation of polarized Hodge structures which degenerates along a normal crossing divisor when certain generation conditions are fulfilled.