Collisions of fat points and applications to interpolation theory

TL;DR

This paper investigates the behavior of colliding fat points in projective space, describing their limits and applying these results to advance interpolation theory and prove new cases of a conjecture.

Contribution

It provides a detailed description of the limits of colliding fat points and applies these findings to solve open problems in interpolation theory.

Findings

Describes limits of fat point collisions in low dimensions

Establishes new cases of Laface-Ugaglia Conjecture

Links collision behavior with interpolation applications

Abstract

We address the problem to determine the limit of the collision of fat points in $\mathbb{P}^n. We give a description of the limit scheme in many cases, in particular in low dimension and multiplicities. The problem turns out to be closely related with interpolation theory, and as an application we exploit collisions to prove some new cases of Laface-Ugaglia Conjecture.