Date/Time
Date(s) - 10/02/2026
10:30 am - 11:30 am

Speaker: Graham Keiper (Catania)

Location: Hamilton Hall, Room 312

Title: Splittings of Ideals of Points in P1 × P1

Abstract: I will discuss recent work done with Elena Guardo (Catania) and Adam Van Tuyl (McMaster) on ideals of points in P1 × P1. Let I_X be the bihomogeneous ideal of a set of finite points X ? P1 × P1. We investigate various notions of “splittings” of the ideal I_X, namely finding ideals J and K such that I_X = J +K, where J and K have prescribed algebraic or geometric properties. We pay particular attention to arithmetically Cohen-Macaulay (ACM) sets of points and introduce the framework of ideals of unions of lines and ACM points in P1 × P1 which allows us to better ”split” these ideals. We also discuss some consequences for the graded Betti numbers of IX in terms of these splittings.