Links of symbolic powers of prime ideals

Abstract

In this paper, we prove the following. Let $$(R, \frak{m})$$ be a Cohen-Macaulay local ring of dimension d ≥ 2. Suppose that either R is not regular or if R is regular assume that d ≥ 3. Let t ≥ 2 be a positive integer. If $$\{\alpha_1, \dots, \alpha_d\}$$ is a regular sequence contained in $$\frak{m}^t$$ , then $$ (\alpha_1, \dots, \alpha_d): \frak{m}^t\subseteq \frak{m}^t.$$ This result gives an affirmative answer to a conjecture raised by Polini and Ulrich.