Software for Computing Multiplier Ideals

Multiplier ideals are interesting for a range of applications in birational geometry, commutative algebra, and algebraic statistics. Unfortunately they are usually very hard to compute. Shibuta's algorithm, implemented in a Macaulay2 package by Christine Berkesch and Anton Leykin, can compute multiplier ideals of modestly sized examples. However, special algorithms for particular classes of ideals can do much better. I describe two Macaulay2 packages being developed for computing multiplier ideals. The first package computes multiplier ideals of monomial ideals, using Howald's theorem, and the second package computes multiplier ideals of monomial curves, using results of Howard Thompson. The second package was written jointly with Claudiu Raicu and Bart Snapp. Both packages use combinatorial algorithms to handle somewhat larger examples more quickly than the general purpose algorithm.