论文标题
分级家庭渐近不变的二元性
Duality for asymptotic invariants of graded families
论文作者
论文摘要
本文的起点是自然数序列的双重性，在轻度假设下，互换次级和超肌肉序列，并反转其渐近生长常数。 我们有动力探索这种序列二元性，因为它在至少两个重要的代数几何环境中自然出现。第一个上下文是Macaulay-Matlis二元性，其中激进理想的符号能力家族的初始程度序列与Castelnuovo-Mummford的规律性值的顺序是由线性形式的力量产生的理想的序列。这种哲学是从埃萨勒姆和艾亚罗比诺的有影响力的论文中得出的。我们将这种二元性推广到理想的差异级过滤。 在不同的方向上，我们在某些理想的符号能力的Castelnuovo-Mumford规则性值和几何启发的序列之间建立了双重性，我们称射流分离序列为二元。我们表明，这种二元性支持了两个重要的几何不变式之间的互惠：多点seshadri常数和一组射影空间中一组点的渐近规则性。
The starting point of this paper is a duality for sequences of natural numbers which, under mild hypotheses, interchanges subadditive and superadditive sequences and inverts their asymptotic growth constants. We are motivated to explore this sequence duality since it arises naturally in at least two important algebraic-geometric contexts. The first context is Macaulay-Matlis duality, where the sequence of initial degrees of the family of symbolic powers of a radical ideal is dual to the sequence of Castelnuovo-Mumford regularity values of a quotient by ideals generated by powers of linear forms. This philosophy is drawn from an influential paper of Emsalem and Iarrobino. We generalize this duality to differentially closed graded filtrations of ideals. In a different direction, we establish a duality between the sequence of Castelnuovo-Mumford regularity values of the symbolic powers of certain ideals and a geometrically inspired sequence we term the jet separation sequence. We show that this duality underpins the reciprocity between two important geometric invariants: the multipoint Seshadri constant and the asymptotic regularity of a set of points in projective space.
