Postulation of general unions of lines and decorated lines

Abstract

A +line A $\subset$ $\mathbb {P}^r$ , $r \geq 3$ , is the scheme A = L $\cup$ $v$ with L a line and $v$ a tangent vector of $\mathbb {P}^r$ supported by a point of L, but not tangent to L. Here we prove that a general disjoint union of lines and +lines has the expected Hilbert function.