Geodesic
On the finite generation of valuation semigroups on toric surfaces
Épijournal de Géométrie Algébrique, Tome 8 (2024)

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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.
DOI : 10.46298/epiga.2024.11407
Classification : 14C20, 14M25, 52B20 
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     author = {Altmann, Klaus and Haase, Christian and K\"uronya, Alex and Schaller, Karin and Walter, Lena},
     title = {On the finite generation of valuation semigroups on toric surfaces},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {8},
     year = {2024},
     doi = {10.46298/epiga.2024.11407},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2024.11407/}
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Altmann, Klaus; Haase, Christian; Küronya, Alex; Schaller, Karin; Walter, Lena. On the finite generation of valuation semigroups on toric surfaces. Épijournal de Géométrie Algébrique, Tome 8 (2024). doi: 10.46298/epiga.2024.11407

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