Affine special Kähler structures in real dimension two

Abstract

We review properties of affine special Kähler structures focusing on singularities of such structures in the simplest case of real dimension two. We describe all possible isolated singularities and corresponding monodromies of the flat symplectic connection, which is a part of a special Kähler structure, near a singularity. Beside numerous local examples, we construct continuous families of special Kähler structures with isolated singularities on the projective line.