Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on Mg
نویسنده
چکیده
Consider genus g curves that admit degree d covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family Y that naturally maps into the moduli space of stable genus g curves Mg. We study the geometry of Y , and produce a combinatorial method by which to investigate its slope, irreducible components, genus and orbifold points. As a by-product of our approach, we find some equalities from classical number theory. Moreover, a correspondence between our method and the viewpoint of square-tiled surfaces is established. We also use our results to study the lower bound for slopes of effective divisors on Mg.
منابع مشابه
Covers of Elliptic Curves and the Moduli Space of Stable Curves
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