摘要翻译：
我们考虑了哪些零维格式变形为不同点集合的问题；等价地，我们问哪个Artinian K-代数变形为域的乘积。我们引入了一个syzygetic不变量，它揭示了正则性为2的零维格式的这个问题。该不变量在一般情况下对光滑性施加了障碍，完全解决了某些低次零维格式的光滑性问题。本文的工具还得到了关于点的Hilbert格式的其他结果，包括在每个嵌入维数D\geq4上最小次的非光滑零维格式的一个刻划。
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英文标题：
《A syzygetic approach to the smoothability of zero-dimensional schemes》
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作者：
Daniel Erman and Mauricio Velasco
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
  We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this question for zero-dimensional schemes of regularity two. This invariant imposes obstructions for smoothability in general, and it completely answers the question of smoothability for certain zero-dimensional schemes of low degree. The tools of this paper also lead to other results about Hilbert schemes of points, including a characterization of nonsmoothable zero-dimensional schemes of minimal degree in every embedding dimension d\geq 4.
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PDF链接：
https://arxiv.org/pdf/0812.3342