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arXiv · 1701.01393

On the n-th row of the graded Betti table of an n-dimensional toric variety

Alexander Lemmens
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Abstract

We prove an explicit formula for the first non-zero entry in the n-th row of the graded Betti table of an n-dimensional projective toric variety associated to a normal polytope with at least one interior lattice point. This applies to Veronese embeddings of projective space where we prove a special case of a conjecture of Ein and Lazarsfeld. 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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Alexander Lemmens. 2017-01-05. On the n-th row of the graded Betti table of an n-dimensional toric variety. https://doi.org/10.1007/s10801-017-0786-y

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