Affine special Kaehler structures in real dimension two

Abstract

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