Computations involving symbolic powers

Abstract

Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously difficult to compute, and there are seemingly simple questions related to symbolic powers that remain open even over polynomial rings. In this paper, we describe a Macaulay2 software package that allows for computations of symbolic powers of ideals and which can be used to study the equality and containment problems, among others.

References in corpus (5)

• Uniform Bounds and Symbolic Powers on Smooth Varieties
• Comparison of symbolic and ordinary powers of ideals
• Resurgences for ideals of special point configurations in ${\mathbf{P}}^N$ coming from hyperplane arrangements
• Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers
• On the containment problem

Cited by in corpus (1)

• Consequences of the packing problem