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摘要翻译：
我们研究了阶为$d$的平面曲线的Severi变体$v_{d,g}$和几何亏格$g$。对应于每一个这样的变体，有一个G$稳定曲线属的单参数族，我们计算它的数值不变量。在Caporaso和Harris的工作的基础上，我们导出了Hodge丛的次的一个递推公式。对于$d$足够大，这些族在$\bar{M}_g$中诱导移动曲线。我们利用这一点导出了$\bar{M}_g$上有效因子斜率的下界。我们的结果的另一个应用是在$v_{d,g}$上的各种枚举问题。
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英文标题：
《Linear sections of the Severi variety and moduli of curves》
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作者：
Maksym Fedorchuk
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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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英文摘要：
We study the Severi variety $V_{d,g}$ of plane curves of degree $d$ and geometric genus $g$. Corresponding to every such variety, there is a one-parameter family of genus $g$ stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For $d$ large enough, these families induce moving curves in $\bar{M}_g$. We use this to derive lower bounds for the slopes of effective divisors on $\bar{M}_g$. Another application of our results is to various enumerative problems on $V_{d,g}$.
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PDF链接：
https://arxiv.org/pdf/0710.1623
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