Covers of an Elliptic Curve E and Curves in ExP1
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 compon...
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| Format: | Others |
| Language: | en |
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Harvard University
2015
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| Online Access: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467298 |
| Summary: | 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 × P1, in a restricted range of degrees. === Mathematics |
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