Space curves that intersect often

Steven P. Diaz

Vol. 123 (1986), No. 2, 263–267

DOI: 10.2140/pjm.1986.123.263

Abstract

In intersection theory one tries to understand X ∩Y in terms of information about how X and Y lie in an ambient variety Z. When the sum of the codimensions of X and Y in Z exceeds the dimension of Z not much is known in this direction. The purpose of this note is to provide some results in perhaps the simplest nontrivial case of this—that of curves in P³ (projective three space). A weaker result for Pⁿ is also obtained. We work over any fixed algebraically closed field of arbitrary characteristic.

Mathematical Subject Classification 2000

Primary: 14H45

Secondary: 14H50

Milestones

Received: 20 March 1985

Revised: 2 July 1985

Published: 1 June 1986