The Nash problem on arc families of singularities
The Nash problem on arc families of singularities
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DOI：
10.1215/s0012-7094-03-12034-7
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发表时间：
2002-07
影响因子：
2.5
通讯作者：
S. Ishii;J. Koll'ar
中科院分区：
文献类型：
--
作者：
S. Ishii;J. Koll'ar
Nash[21]证明了通过奇点的圆弧空间的每个不可约分支对应于出现在每种分解上的一个例外因子。他问，反之是否也成立：每个这样的特殊因子都对应于一个弧族吗？我们证明了反之对于环面奇点是成立的，但一般是不成立的。
Nash [21] proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that appears on every resolution. He asked if the converse also holds: Does every such exceptional divisor correspond to an arc family? We prove that the converse holds for toric singularities but fails in general.