Multigraded Betti numbers of Veronese embeddings
Commutative Algebra
2026-03-12 v2 Algebraic Geometry
Combinatorics
Abstract
In this paper, we study the multigraded Betti numbers of Veronese embeddings of projective spaces. Due to Hochster's formula, we interpret these multigraded Betti numbers in terms of the homology of certain simplicial complexes. By analyzing these simplicial complexes and applying Forman's discrete Morse theory, we derive vanishing and non-vanishing results for these multigraded Betti numbers.
Keywords
Cite
@article{arxiv.2511.18994,
title = {Multigraded Betti numbers of Veronese embeddings},
author = {Christian Haase and Zongpu Zhang},
journal= {arXiv preprint arXiv:2511.18994},
year = {2026}
}
Comments
17 pages. Included references to bounded degree (hyper-)graph complexes