C ∗-equivariant degenerations of curves and normal surface singularities with C ∗-action
C ∗-equivariant degenerations of curves and normal surface singularities with C ∗-action
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发表时间：
2013
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通讯作者：
T. Tomaru;T. Tomaru
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作者：
T. Tomaru;T. Tomaru
本文给出了C上紧复曲线族的C∗等变退化族的定义，称之为C∗曲线族。给出了它们的正则构造方法，并用C-∗作用量证明了它们与法向曲面奇点之间关系的一些结果。我们还定义了P_1上紧复曲线的C-∗等变退化族。由此，可以自然地引入曲线的对偶C∗-铅笔的概念。结合它，我们证明了具有C-∗作用的正规曲面奇点的循环覆盖的一个对偶性。
This paper presents a definition of C∗-equivariant degeneration families of compact complex curves over C. Those families are called C∗-pencils of curves. We give the canonical method to construct them and prove some results on relations between them and normal surface singularities with C∗-action. We also define C∗-equivariant degeneration families of compact complex curves over P1. From this, it is possible to introduce a notion of dual C∗-pencils of curves naturally. Associating it, we prove a duality for cyclic covers of normal surface singularities with C∗-action.