Klaus Altmann ; Christian Haase ; Alex Küronya ; Karin Schaller ; Lena Walter - On the finite generation of valuation semigroups on toric surfaces

epiga:11407 - Épijournal de Géométrie Algébrique, May 12, 2024, Volume 8 - https://doi.org/10.46298/epiga.2024.11407
On the finite generation of valuation semigroups on toric surfacesArticle

Authors: Klaus Altmann ; Christian Haase ; Alex Küronya ; Karin Schaller ; Lena Walter

    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.


    Volume: Volume 8
    Published on: May 12, 2024
    Accepted on: December 15, 2023
    Submitted on: May 31, 2023
    Keywords: Mathematics - Algebraic Geometry,14C20, 14M25, 52B20

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