Mixed trTLEP-structures and mixed Frobenius structures

TL;DR

This paper introduces mixed trTLEP-structures and demonstrates their role in inducing mixed Frobenius manifolds, generalizing existing theorems and linking Hodge structures to B-models.

Contribution

It defines mixed trTLEP-structures and proves their connection to mixed Frobenius manifolds, extending Hertling and Manin's reconstruction theorem.

Findings

Mixed trTLEP-structures induce mixed Frobenius manifolds under certain conditions.

Graded polarizable variation of mixed Hodge structures with H^2-generation produce mixed Frobenius manifolds.

Existence of mixed Frobenius manifolds associated to local B-models.

Abstract

We introduce the notion of mixed trTLEP-structures and prove that a mixed trTLEP-structure with some conditions naturally induces a mixed Frobenius manifold. This is a generalization of the reconstruction theorem of Hertling and Manin. As a special case, we also show that a graded polarizable variation of mixed Hodge structure with $H^2$-generation condition gives rise to a family of mixed Frobenius manifolds. It implies that there exist mixed Frobenius manifolds associated to local B-models.