Stable log surfaces and limits of quartic plane curves
Stable log surfaces and limits of quartic plane curves
复制标题
稳定对数曲面和四次平面曲线的极限
DOI：
10.1007/s002290050213
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发表时间：
1999
影响因子：
0.6
通讯作者：
B. Hassett
中科院分区：
文献类型：
--
作者：
B. Hassett
摘要：设C∧2为d≥4次的光滑平面曲线。我们把对（}2，C）看作稳定的对数曲面，是点稳定曲线的高维类似物。利用对数最小模型程序，Kollár， Shepherd-Barron和Alexeev已经为稳定的对数曲面构造了投影模空间。不幸的是，这些模空间的明确例子很少。本文的目的是给出小次平面曲线的这些空间的具体描述。特别地，我们证明了四次平面曲线对应的稳定对数曲面的模空间与三格稳定曲线的模空间重合。
Abstract:Let C⊂ℙ2 be a smooth plane curve of degree d≥ 4. We regard pairs (ℙ}2,C) as stable log surfaces, higher-dimensional analogs to pointed stable curves. Using the log minimal model program, Kollár, Shepherd-Barron, and Alexeev have constructed projective moduli spaces for stable log surfaces. Unfortunately, few explicit examples of these moduli spaces are known. The purpose of this paper is to give a concrete description of these spaces for plane curves of small degree. In particular, we show that the moduli space of stable log surfaces corresponding to quartic plane curves coincides with the moduli space of stable curves of genus three.