Links of symbolic powers of prime ideals

Links of symbolic powers of prime ideals

In this paper, we prove the following. Let (R,m) be a Cohen-Macaulay local ring of dimension d ≥ 2. Suppose that either R is not regular or R is regular with d ≥ 3. Let t ≥ 2 be a positive integer. If {α1, . . . , αd} is a regular sequence contained in m, then (α1, . . . , αd) : m t ⊆ m. This result gives an affirmative answer to a conjecture raised by Polini and Ulrich.

Comparing Powers and Symbolic Powers of Ideals

We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...

Links of Prime Ideals

We exhibit the elementary but somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals. It leads to the construction of a bountiful set of Cohen–Macaulay Rees algebras.

Symbolic Powers of Ideals in k[PN]

Generalized Test Ideals and Symbolic Powers

In [HH7], developing arguments in [HH5], Hochster and Huneke used classical tight closure techniques to prove a fine behavior of symbolic powers of ideals in regular rings. In this paper, we use generalized test ideals, which are a characteristic p analogue of multiplier ideals, to give a generalization of Hochster-Huneke's results.