Prym curves with a vanishing theta-null

Abstract

If the theta-null divisor ${\Theta }_{\mathrm{null}}$ is moved to the Prym moduli space through the diagram ${\mathcal{S}}_g^{+}\to {\mathcal{M}}_g\leftarrow {\mathcal{R}}_g$, it splits into two irreducible components ${\mathcal{P}}_{\mathrm{null}}^{+}$ and ${\mathcal{P}}_{\mathrm{null}}^{-}$. Using test curve techniques, we compute the class of the closure of each of these components in terms of the generating classes of $\mathrm{Pic}({\overline{\mathcal{R}}}_g{)}_{\mathbb{Q}}$.

47 pages, second part of the author's PhD thesis