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arXiv · 2209.06044

On the finite generation of valuation semigroups on toric surfaces

Klaus Altmann·Christian Haase·Alex Küronya·Karin Schaller·Lena Walter
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Abstract

We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytope such that none of the valuation semigroups of the associated polarized toric variety coming from one-parameter subgroups and centered at a non-toric point are finitely generated.

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Klaus Altmann, Christian Haase, Alex Küronya, Karin Schaller, Lena Walter. 2022-09-13. On the finite generation of valuation semigroups on toric surfaces. https://doi.org/10.46298/epiga.2024.11407

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