STABILITY OF DEPTH AND STANLEY DEPTH OF SYMBOLIC POWERS OF SQUAREFREE MONOMIAL IDEALS

摘要

Let K be a field and let S = K[x(1), ..., x(n)] be the polynomial ring in n variables over K. Assume that I subset of S is a squarefree monomial ideal. For every integer k >= 1, we denote the k-th symbolic power of I by I-(k). Recently, Montano and Nunez-Betancourt (2018), and independently Nguyen and Trung (to appear), proved that for every pair of integers k, i >= 1,