The Hurwitz space of covers of an elliptic curve $E$ and the Severi variety of curves in $E\times {\mathbb{P}}^1$

Gabriel Bujokas

We describe the hyperplane sections of the Severi variety of curves in $E\times {\mathbb{P}}^1$ in a similar fashion to Caporaso-Harris' seminal work. From this description we almos…