D. Chen

Covers of elliptic curves and the moduli space of curves

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.