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Abstract
Consider genus g curves that admit degree d covers of an elliptic curve. Varying a branch point, we get a one-parameter family W of simply branched covers. Varying the target elliptic curve, we get another one-parameter family Y of covers that have a unique branch point. We investigate the geometry of W and Y by using admissible covers to study their slopes, genera and components. The results can be applied to study slopes of effective divisors on the moduli space of stable genus g curves.
Received: 2008-08-09
Revised: 2009-06-10
Published Online: 2010-10-19
Published in Print: 2010-December
© Walter de Gruyter Berlin · New York 2010