Local models of isolated singularities for affine special K\"ahler structures in dimension two

TL;DR

This paper constructs local models for isolated singularities in affine special K"ahler structures in two dimensions, assuming the holomorphic cubic form is well-behaved, and computes the holonomy of the associated flat symplectic connection.

Contribution

It provides explicit local models for singularities in 2D special K"ahler structures under certain conditions and calculates the holonomy of the related flat symplectic connection.

Findings

Explicit local models for singularities in 2D special K"ahler structures.

Holonomy computations of the flat symplectic connection.

Conditions on the holomorphic cubic form for model construction.

Abstract

We construct local models of isolated singularities for special K\"ahler structures in real dimension two assuming that the associated holomorphic cubic form does not have essential singularities. As an application we compute the holonomy of the flat symplectic connection, which is a part of the special K\"ahler structure.