摘要翻译:
如果X是多射影空间p^n1x…xp^nr中的有限点集,且r>=2,则X可能是也可能不是算术Cohen-Macaulay(ACM)。对于p^1×p^1中的点集,ACM点集有几种分类。本文研究了这些分类在任意多射影空间中的自然推广。我们证明了在p^1×p^1中对ACM点的每一种分类都不能推广到一般情况。我们也给出了点集是ACM的一些新的充要条件。
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英文标题:
《ACM sets of points in multiprojective space》
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作者:
Elena Guardo and Adam Van Tuyl
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最新提交年份:
2007
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分类信息:
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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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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英文摘要:
If X is a finite set of points in a multiprojective space P^n1 x ... x P^nr with r >= 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For sets of points in P^1 x P^1 there are several classifications of the ACM sets of points. In this paper we investigate the natural generalizations of these classifications to an arbitrary multiprojective space. We show that each classification for ACM points in P^1 x P^1 fails to extend to the general case. We also give some new necessary and sufficient conditions for a set of points to be ACM.
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PDF链接:
https://arxiv.org/pdf/0707.3138