Casas-Alvero conjecture in computational algebraic geometry

TL;DR

This paper uses computational algebraic geometry techniques to analyze polynomial derivatives, establishing regular sequences and calculating variety dimensions, ultimately proving the Casas-Alvero conjecture.

Contribution

It introduces a novel algebraic geometric approach to prove the Casas-Alvero conjecture using combinatorial and normalization methods.

Findings

Polynomials form regular sequences easily

Calculated the dimension of parameterized varieties

Provided a proof for the Casas-Alvero conjecture

Abstract

We study varieties defined by parameterizing polynomials of derivatives through a computational algebro-geometric approach, especially relying on Combinatorial Nullstellensatz and Noether normalization. We establish that these polynomials form regular sequences easily. This allows us to calculate the dimension of thus defined varieties and consequently give a proof to the Casas-Alvero conjecture.