A formula for the core of certain strongly stable ideals

The core of an ideal is the intersection of all of its reductions. The core is a natural object to study from the point of view of blow-up algebras and integral closure; and it also has geometric significance coming, for example, from its connection to adjoint and multiplier ideals. In general, the core is difficult to describe explicitly. In this paper, we investigate a particular family of strongly stable ideals. We prove that ideals in this family satisfy an Artin–Nagata property, yet fail to satisfy other, stronger standard depth conditions. We then show that there is a surprisingly simple explicit formula for the core of these ideals.