On the postulation of lines and a fat line

TL;DR

This paper proves that a union of r general lines and one fat line in projective 3-space imposes independent conditions on high-degree forms, extending previous results on lines and double lines.

Contribution

It extends prior work by showing independence conditions for unions of lines and a fat line in P^3, with bounds independent of the number of lines.

Findings

Union of r lines and one fat line imposes independent conditions on forms of high degree

Bound on degree d is independent of the number of lines

Extends previous results on lines and double lines in projective space

Abstract

In this note we show that the union of $r$ general lines and one fat line in ${\mathbb P}^3$ imposes independent conditions on forms of sufficiently high degree $d$, where the bound on $d$ is independent of the number of lines. This extends former results of Hartshorne and Hirschowitz on unions of general lines, and of Aladpoosh on unions of general lines and one double line.