The Koszul homology algebra of the second Veronese is generated by the lowest strand

TL;DR

This paper proves that the Koszul homology algebra of the second Veronese subalgebra is generated by classes related to the lowest linear strand syzygies, revealing a fundamental algebraic structure.

Contribution

It establishes that the entire Koszul homology algebra is generated by the lowest strand syzygies, a new insight into the algebraic structure of the second Veronese.

Findings

Koszul homology algebra is generated by lowest strand syzygies

The result holds over fields of characteristic zero

Provides a structural understanding of the second Veronese algebra

Abstract

We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology classes corresponding to the syzygies of the lowest linear strand.