A result on resolutions of Veronese embeddings

TL;DR

This paper investigates the syzygies of Veronese embeddings, proving that certain line bundles satisfy Property N_p under specific conditions, advancing understanding of their algebraic properties.

Contribution

It establishes that O(3) on P^n satisfies Property N_4 for all n and characterizes when O(d) on P^n satisfies N_p based on lower-dimensional cases.

Findings

O(3) on P^n satisfies N_4 for all n

O(d) on P^n satisfies N_p iff O(d) on P^p satisfies N_p

Advances understanding of syzygies in Veronese embeddings

Abstract

This paper deals with syzygies of the ideals of the Veronese embeddings. We prove that O(3) on P^n satisfies Property N_4 for every n. Besides we prove that O(d) on P^n satisfies N_p for all n >= p iff O(d) on P^p satisfies N_p.