Simply branched covers of an elliptic curve and the moduli space of curves

Details Simply branched covers of an elliptic curve and the moduli space of curves Simply branched covers of an elliptic curve and the moduli space of curves

2008-06-04

arxiv.org/abs/0806.0674v1

Mathematics

Algebraic Geometry

21 pages, 11 figures. This is a sequel of arXiv:0704.3994. Comments are welcome

Scientific paper

Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g-2 points. Vary a branch point and the locus of such covers forms a one-parameter family W. We investigate the geometry of W by using admissible covers to study its slope, genus and components. The results can also be applied to study slopes of effective divisors on the moduli space of genus g curves.

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