Deformation of theta characteristics
- Emre Sertöz (MPI MiS, Leipzig)
Abstract
Any non-hyperelliptic curve of genus g admits an embedding into the projective space of dimension g-1 via its space of holomorphic differentials. This is the only embedding that can be consistently defined over every family of non-hyperelliptic curves and is deservedly called the canonical embedding.
The general curve of genus g, canonically embedded in
We will demonstrate how such questions can be answered by degenerating a smooth curve to a nodal curve and by following these points of tangency all the way to the nodal curve. Theta characteristics provide us with a convenient language and the means to study infinitesimal perturbations of such degenerations.