论文标题
残留的交叉点和线性力量
Residual Intersections and Linear Powers
论文作者
论文摘要
如果我在Gorenstein环S和S/I中是Cohen-Macaulay中的理想，那么任何链接的理想I'都是如此。但是，此类陈述仅在非常限制的假设下仅在较高的编成率的剩余相交中，即使是像n> 3时通用2 x n矩阵的理想l_n的理想L_N一样简单的理想。 在本文中，我们启动了对不同类型的Cohen-Macaulay属性的研究，该属性具有某些最大（最大（有趣）的编纂的一般残留相互作用，比I的分析率少于I。是S/K上方具有线性分辨率的S/K的自我最大Cohen-Macaulay模块。 本文的技术核心是分析扩散1的理想1，其高力量是线性呈现的。
If I is an ideal in a Gorenstein ring S and S/I is Cohen-Macaulay, then the same is true for any linked ideal I'. However, such statements hold for residual intersections of higher codimension only under very restrictive hypotheses, not satisfied even by ideals as simple as the ideal L_n of minors of a generic 2 x n matrix when n>3. In this paper we initiate the study of a different sort of Cohen-Macaulay property that holds for certain general residual intersections of the maximal (interesting) codimension, one less than the analytic spread of I. For example, we prove that if K is the residual intersection of L_n by 2n-3 general quadratic forms in L_n, then S/K is integrally closed with isolated singularity and I^{n-3} S/K is a self-dual Maximal Cohen-Macaulay module over S/K with linear free resolution over S. The technical heart of the paper is a result about ideals of analytic spread 1 whose high powers are linearly presented.
