Complete intersections primitive structures on space curves

TL;DR

This paper establishes numerical criteria for space curves in P3 to possess primitive multiple structures that are complete intersections, advancing understanding of their geometric and algebraic properties.

Contribution

It introduces specific numerical conditions characterizing when a space curve admits a primitive multiple structure as a complete intersection.

Findings

Provides criteria for primitive multiple structures on space curves.

Characterizes when such structures are set-theoretic complete intersections.

Enhances understanding of the geometry of space curves with multiple structures.

Abstract

A multiple (loc. Cohen Macaulay) structure, X, on a space curve C in P3 is said to be primitive if X is locally contained in a smooth surface. We give numerical conditions for C to be a "primitive" set theoretic complete intersection (i.e. to have a primitive multiple structure which is a complete intersection).