Finite sets of points in P4 with special projection properties

Abstract

In this note we introduce the notion of (b, d)-geprofi sets and study their basic properties. These are sets of bd points in P4 whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree b and a surface of degree d. We show that such nontrivial sets exist if and only if b >= 4 and d >= 2. Somewhat surprisingly, for infinitely many values of b and d there exist such sets in linear general position. The note contains open questions and problems.