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摘要翻译：
考虑G$曲线的属，它允许D$复盖到椭圆曲线，只在一点分枝，分支类型固定。这类覆盖的轨迹形成一个单参数族$Y$，它自然映射到稳定亏格$g$曲线$\bar{\mathcal M}_{g}$的模空间中。我们研究了$y$的几何学，并给出了一种组合方法来研究它的斜率、不可约分量、亏格和轨道点。作为我们方法的副产品，我们从经典数论中找到了一些等式。此外，我们的方法与平铺曲面的观点建立了对应关系。我们还利用我们的结果研究了$\bar{\mathcal M}_{g}$上有效因子斜率的下界。
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英文标题：
《Covers of Elliptic Curves and the Lower Bound for Slopes of Effective
Divisors on $\bar{\mathcal M}_{g}$》
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作者：
Dawei Chen
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Geometric Topology 几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
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 $\bar{\mathcal M}_{g}$. 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 $\bar{\mathcal M}_{g}$.
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PDF链接：
https://arxiv.org/pdf/0704.3994
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