Limiting Behaviour of Symbolic Powers

Abstract: At the heart of many problems in Commutative Algebra and Algebraic Geometry is the difference between symbolic and regular powers of a homogeneous ideal. One way to find failures of containments between these powers is to use an asymptotic approach and look at a special limit called the Waldschmidt constant. This limit was first introduced as a way to estimate the lowest degree of a hypersurface vanishing at all the points of a variety to a given order. However, this limit is challenging to compute and so it is natural to focus our attention on special ideals to gain insight. In this talk we will give some interpretations of the Waldschmidt constant of a monomial ideal which allow us to determine this limit in a number of cases. This is joint work from two projects: the first with R. Embree, H. T. Hà, and A. Hoefel and the second with C. Bocci, E. Guardo, B. Harbourne, M. Janssen, U. Nagel, A. Seceleanu, A. Van Tuyl, and T. Vu.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca