Isolated singularities of affine special K\"ahler metrics in two dimensions

TL;DR

This paper classifies isolated singularities of affine special Kähler metrics in two dimensions, showing only two types occur under certain conditions, and provides explicit examples of these metrics.

Contribution

It establishes a classification of isolated singularities for affine special Kähler metrics in two dimensions when the associated cubic form is well-behaved, and constructs explicit examples.

Findings

Only two types of isolated singularities occur under the given conditions.

Explicit examples of affine special Kähler metrics with these singularities are constructed.

Abstract

We prove that there are just two types of isolated singularities of special K\"ahler metrics in real dimension two provided the associated holomorphic cubic form does not have essential singularities. We also construct examples of such metrics.