Abstract The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces P 1 × P 1 , we investigate which sets of points have a virtual resolution that is a Koszul complex on a regular sequence. This paper provides conditions on sets of points; some of which guarantee the points have this property, and some of which guarantee the points do not have this property.

中文翻译：

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P1×P1 中的虚拟完全交叉点

摘要 射影空间中完全交的坐标环的最小自由分辨率是正则序列上的Koszul复形。在射影空间 P 1 × P 1 的乘积中，我们研究了哪些点集的虚拟分辨率是规则序列上的 Koszul 复形。本文提供了点集的条件；有的保证积分有这个属性，有的保证积分没有这个属性。