Covers of Elliptic Curves and the Moduli Space of Stable Curves
نویسنده
چکیده
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.
منابع مشابه
Simply Branched Covers of an Elliptic Curve and the Moduli Space of Curves
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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