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arXiv · 2511.18994

Multigraded Betti numbers of Veronese embeddings

Christian Haase·Zongpu Zhang
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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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Christian Haase, Zongpu Zhang. 2025-11-24. Multigraded Betti numbers of Veronese embeddings. https://arxiv.org/abs/2511.18994

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