Abstract
We prove an explicit formula for the first nonzero entry in the n-th row of the graded Betti table of an n-dimensional projective toric variety associated with a normal polytope with at least one interior lattice point. This applies to Veronese embeddings of \(\mathbb {P}^n\). We also prove an explicit formula for the entire n-th row when the interior of the polytope is one-dimensional. All results are valid over an arbitrary field k.
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Acknowledgements
This article is part of my Ph.D. thesis which is funded by the Research Foundation Flanders (FWO). It was my colleagues Wouter Castryck and Filip Cools who noticed patterns in Betti tables of certain toric surfaces, which motivated me to find an explicit basis. I am also grateful to the referee for carefully reading my article and making many useful suggestions. I also want to thank Milena Hering for bringing the article [7] to my attention.
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The author is supported by the Flemmish Research Council (FWO - Vlaanderen).
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Lemmens, A. On the n-th row of the graded Betti table of an n-dimensional toric variety. J Algebr Comb 47, 561–584 (2018). https://doi.org/10.1007/s10801-017-0786-y
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DOI: https://doi.org/10.1007/s10801-017-0786-y