Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on $\bar{\mathcal M}_{g}$

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dc.creatorChen, Dawei
dc.date2007-04-30
dc.date.accessioned2026-07-07T07:58:49Z
dc.date.available2026-07-07T07:58:49Z
dc.descriptionConsider 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 $\bar{\mathcal M}_{g}$. 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 $\bar{\mathcal M}_{g}$.
dc.description41 pages, 19 figures
dc.identifierhttps://arxiv.org/abs/0704.3994
dc.identifierhttp://arxiv.org/abs/0704.3994
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128146
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subject14H10; 14H30; 05A15; 05E15
dc.titleCovers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on $\bar{\mathcal M}_{g}$
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