Frobenius 3-Folds via Singular Flat 3-Webs

TL;DR

This paper provides a geometric interpretation of solutions to the associativity equation using web theory and constructs Frobenius 3-fold germs with specific geometric properties.

Contribution

It introduces a novel geometric approach to Frobenius 3-folds via singular 3-webs with symmetry and flat connection conditions.

Findings

Constructed Frobenius 3-fold germs from singular 3-webs

Established conditions for web germs with symmetries and flatness

Linked web theory to Frobenius manifold structures

Abstract

We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the Chern connection form is holomorphic, 3) the curvature form vanishes identically.