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

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.

arXiv comment21 pages, 11 figures. This is a sequel of arXiv:0704.3994. Comments are welcome

References in corpus (6)

• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
• Moduli of Trigonal Curves
• Moduli spaces of curves with linear series and the slope conjecture
• Descendent bounds for effective divisors on the moduli space of curves
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• Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on ${\bar{\mathcal{M}}}_g$