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arXiv · 0806.0674

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

Dawei Chen
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Abstract

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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Dawei Chen. 2008-06-04. Simply branched covers of an elliptic curve and the moduli space of curves. https://arxiv.org/abs/0806.0674

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