Conjectures and computations about Veronese syzygies

TL;DR

This paper proposes new conjectures about the structure of Veronese syzygies in projective spaces, supported by computational experiments using advanced numerical linear algebra and distributed computing techniques.

Contribution

It introduces several conjectures on Veronese syzygies and develops novel computational methods to generate and analyze data for these algebraic structures.

Findings

Formulated new conjectures on Veronese syzygies

Developed numerical linear algebra techniques for large-scale computations

Generated experimental data supporting the conjectures

Abstract

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed computation technique for computing and synthesizing new cases of Veronese embeddings for $\mathbb{P}^2$.