The geproci property in positive characteristic

Abstract

The geproci property is a recent development in the world of geometry. We call a set of points Z ⊆ P k 3 Z\subseteq \mathbb {P}_k^3 an ( a , b ) (a,b) -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P P to a plane is a complete intersection of curves of degrees a ≤ b a\leq b . Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids.

In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.