Examples of limits of Frobenius (type) structures: the singularity case

TL;DR

This paper explores the behavior of Frobenius type structures near boundaries, providing examples and analyzing the existence of limit Frobenius manifolds, including a case with a logarithmic Frobenius manifold.

Contribution

It presents explicit examples of Frobenius type structures on the punctured plane and investigates their limits, advancing understanding of boundary behavior in these structures.

Findings

Examples of Frobenius type structures on the punctured plane

Analysis of their limits at the boundary

Existence of a limit Frobenius manifold and a logarithmic Frobenius manifold

Abstract

We give examples of families of Frobenius type structures on the punctured plane and we study their limits at the boundary. We then discuss the existence of a limit Frobenius manifold. We also give an example of a logarithmic Frobenius manifold.