Postulation of disjoint unions of lines and a multiple point, II

TL;DR

This paper proves that a general union of one multiple point and disjoint lines in projective 3-space has the expected Hilbert function, confirming a conjecture by Carlini, Catalisano, and Geramita.

Contribution

It establishes the expected Hilbert function for unions of a multiple point and disjoint lines in -space, confirming a prior conjecture.

Findings

The union has the expected Hilbert function.

The conjecture by Carlini, Catalisano, and Geramita is proven.

The result applies to general configurations in -space.

Abstract

We study the postulation of a general union $X\subset \mathbb {P}^3$ of one m-point $mP$ and $t$ disjoint lines. We prove that it has the expected Hilbert function, proving a conjecture by E. Carlini, M. V. Catalisano and A. V. Geramita.