Log canonical models for the moduli space of curves: The first divisorial contraction
Log canonical models for the moduli space of curves: The first divisorial contraction
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曲线模空间的对数正则模型：第一次除数收缩
DOI：
10.1090/s0002-9947-09-04819-3
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发表时间：
2006
影响因子：
1.3
通讯作者：
Donghoon Hyeon
中科院分区：
文献类型：
--
作者：
B. Hassett;Donghoon Hyeon
在本文中，我们开始我们的研究的对数正则模型（MG，αδ），因为我们减少α从1到0。证明了对于第一个临界值α = 9/11，对数正则模型同构于以节点和尖点为奇点的伪稳定曲线的模空间。我们还表明，α = 7/10是下一个临界值，即，对数正则模型在区间（7/10，9/11）内保持不变。在附录中，我们开发了一个理论的日志规范模型的堆栈，解释了如何这些可以表示在粗模空间。
In this paper, we initiate our investigation of log canonical models for (M g , αδ) as we decrease α from 1 to 0. We prove that for the first critical value α = 9/11, the log canonical model is isomorphic to the moduli space of pseudostable curves, which have nodes and cusps as singularities. We also show that α = 7/10 is the next critical value, i.e., the log canonical model stays the same in the interval (7/10,9/11]. In the appendix, we develop a theory of log canonical models of stacks that explains how these can be expressed in terms of the coarse moduli space.