| We describe the hyperplane sections of the Severi variety of curves in ExP1 in a similar fashion to Caporaso--Harris' seminal work. From this description we almost get a recursive formula for the Severi degrees-----we get the terms, but not the coefficients.;As an application, we determine the components of the Hurwitz space of simply branched covers of a genus one curve. In return, we use this characterization to describe the components of the Severi variety of curves in E x P1, in a restricted range of degrees. |
