Separators of points in a multiprojective space

TL;DR

This paper explores properties of separators of points in multiprojective spaces, establishing multigraded analogs of known results connecting Hilbert functions, degrees of separators, and free resolutions.

Contribution

It introduces multigraded analogs of classical results, linking separator degrees to Hilbert functions and free resolutions in multiprojective spaces.

Findings

Proved multigraded analogs of Hilbert function relations.

Connected degrees of separators to shifts in free resolutions.

Extended known results to the multiprojective setting.

Abstract

In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \{P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ideal of points.