Covers of elliptic curves and the moduli space of curves
Covers of elliptic curves and the moduli space of curves
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D. Chen, Harvard University
Fine Hall 214
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 genus $g$ curves $\bar{M}_g$. We study the geometry of $Y$, and produce a combinatorial method by which to investigate its slope, irreducible components and genus. The results can be used to study the lower bound for slopes of effective divisors on $\bar{M}_g$.