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摘要翻译：
考虑n次具有d个节点和k个尖点的不可约平面曲线族为奇点。设W是S的不可约分量，我们考虑从W到亏格G=(n-1)(n-2)/2-d-k曲线模空间的自然有理映射。我们定义“W的模数”为W的像相对于这个映射的维数。若W的期望维数等于3n+g-1-k，则W的模数至多等于min(3g-3,3g-3+rho-k),dove\rho是g属光滑曲线上n次2维线性级数的Brill-Neother数。如果等式成立，我们说W有期望的模数。本文构造了以节点和尖点为奇点的不可约平面曲线族的例子，这些奇点具有期望的模数和非正的Brill-Noether数。
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英文标题：
《Number of moduli of irreducible families of plane curves with nodes and
cusps》
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作者：
Concettina Galati
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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：
Consider the family S of irreducible plane curves of degree n with d nodes and k cusps as singularities. Let W be an irreducible component of S. We consider the natural rational map from W to the moduli space of curves of genus g=(n-1)(n-2)/2-d-k. We define the "number of moduli of W" as the dimension of the image of W with respect to this map. If W has the expected dimension equal to 3n+g-1-k, then the number of moduli of W is at most equal to the min(3g-3, 3g-3+\rho-k), dove \rho is the Brill-Neother number of the linear series of degree n and dimension 2 on a smooth curve of genus g. We say that W has the expected number of moduli if the equality holds. In this paper we construct examples of families of irreducible plane curves with nodes and cusps as singularities having expected number of moduli and with non-positive Brill-Noether number.
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PDF链接：
https://arxiv.org/pdf/0704.0618
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