Tavares Bujokas, Gabriel2015-07-172015-052015-04-302015Tavares Bujokas, Gabriel. 2015. Covers of an Elliptic Curve E and Curves in ExP1. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467298We 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 × P1, in a restricted range of degrees.application/pdfenMathematicsThesis or Dissertation2015-07-17