Hilbert schemes and cyclic quotient surface singularities
Hilbert schemes and cyclic quotient surface singularities
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希尔伯特方案和循环商表面奇点
DOI：
10.14492/hokmj/1350911925
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发表时间：
2001
影响因子：
0.5
通讯作者：
R. Kidoh
中科院分区：
文献类型：
--
作者：
R. Kidoh
.设G是GL（2，C）的n阶有限循环子群，不含反射.设A ^{2}为复平面。考虑Hi 1b ^{n}（A ^{2}）的某个子概型Hi 1b ^{G}（A ^{2}）由长度为n的G -不变零维子概型组成.我们描述了Hi 1b ^{G}（A^{2}）的结构，并证明了这是商曲面奇点A ^{2}/G的最小分解.
. Let G be a finite cyclic subgroup of GL(2, C) of order n which contains no reflections. Let A ^{2} be the complex affine plane. We consider a certain subscheme Hi1b ^{G}(A^{2}) of Hi1b ^{n}(A^{2}) consisting of G -invariant zer0-dimensional subschemes of length n . We describe the structure of Hi1b ^{G}(A^{2}) and prove this is the minimal resolution of the quotient surface singularity A ^{2}/G .