A duality theorem for syzygies of Veronese ideals
Abstract
We prove a duality theorem for simplicial complexes arising from a combinatorial construction we define, which applies to the squarefree monomial complexes for Veronese ideals of projective spaces and weighted projective spaces. Our theorem yields a formula for the multigraded Betti numbers of these Veronese ideals in terms of the reduced homology groups of these complexes which is dual to one given by Bruns and Herzog. We apply this formula in several ways, including by giving an algorithm for finding the highest syzygy of such a Veronese ideal.
Keywords
Cite
@article{arxiv.1311.5653,
title = {A duality theorem for syzygies of Veronese ideals},
author = {Stepan Paul},
journal= {arXiv preprint arXiv:1311.5653},
year = {2014}
}
Comments
The first version of this preprint did not reflect the fact that one of the main theorems had been previously been proven in another publication--a fact which was subsequently brought to the author's attention. See the footnote on page 1