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 \({\mathbb{X}}\) and \({\mathbb{X}} \backslash \{P\}\) 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.
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Guardo, E., Van Tuyl, A. Separators of points in a multiprojective space. manuscripta math. 126, 99–113 (2008). https://doi.org/10.1007/s00229-008-0165-z
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DOI: https://doi.org/10.1007/s00229-008-0165-z