Plane curves with prescribed triple points: a toric approach

TL;DR

This paper introduces a new proof for the triple points interpolation problem in the projective plane using toric degenerations, and identifies relevant toric surfaces for this approach.

Contribution

It provides a novel toric degeneration method to address the triple points interpolation problem and classifies toric surfaces suitable for this technique.

Findings

New proof of triple points interpolation in the projective plane

Complete classification of toric surfaces used in degenerations

Identification of toric components relevant to the problem

Abstract

We will use toric degenerations of the projective plane ${{\mathbb{P}}^ 2}$ to give a new proof of the triple points interpolation problems in the projective plane. We also give a complete list of toric surfaces that are useful as components in this degeneration.