Multigraded Betti numbers of Veronese embeddings
Christian Haase, Zongpu Zhang
TL;DR
This paper investigates the multigraded Betti numbers of Veronese embeddings of projective spaces, using Hochster's formula and discrete Morse theory to determine their vanishing properties.
Contribution
It introduces a novel approach combining Hochster's formula with Forman's discrete Morse theory to analyze Betti numbers of Veronese embeddings.
Findings
Derived vanishing and non-vanishing results for multigraded Betti numbers
Connected Betti number properties to homology of simplicial complexes
Applied discrete Morse theory to simplify complex homological computations
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.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics