Covers of elliptic curves and slopes of effective divisors on the moduli space of curves
by Chen, Dawei, Ph.D., HARVARD UNIVERSITY, 2008, 60 pages; 3312313

Abstract:

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 [special characters omitted]. We study the geometry of Y, and produce a combinatorial method by which to investigate its slope, irreducible components, genus and orbifold points. 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 [special characters omitted].

 
AdviserJoe Harris
SchoolHARVARD UNIVERSITY
SourceDAI/B 69-05, p. , Aug 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3312313
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