Tubes in three–dimensional projective spaces

Abstract

A partial tube in PG(3, q) is a pair T = {L, L}, where {L} ∪ L is a collection of mutually disjoint lines of PG(3, q) with the property that for each plane π of PG(3, q) through L, the intersection of π with the lines of L is an arc. Here, we generalize the notion of partial tube allowing the ground field to be any algebraically closed field. To a generalized partial tube we will associate an irreducible surface of degree d in P 3 K providing upper bounds on d. (2000): 51E20. Mathematics Subject Classification