Associated primes of powers of monomial ideals
- Jutta Rath (MPI MiS, Leipzig)
Abstract
In general, the set of associated primes of an ideal changes when looking at powers of the ideal. These changes have been studied in many different settings. In the Noetherian case, it is well known that the sequence of associated primes of powers of an ideal stabilizes.
It is not known when this stabilization occurs; however, some classes of ideals are well understood. For example, the associated primes of powers of edge ideals of finite simple graphs can be fully described by the structure of the graph. This talk focuses on the stabilization of associated primes of powers of monomial ideals and presents a technique to develop upper bounds for the power of an ideal after which the sequence is non-increasing. This approach is based on describing membership of monomials in ideals via solutions of systems of linear inequalities.
Based on a joint work with Roswitha Rissner and Clemens Heuberger.
