On the finite generation of valuation semigroups on toric surfaces
Algebraic Geometry
2026-05-27 v3
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.
Keywords
Cite
@article{arxiv.2209.06044,
title = {On the finite generation of valuation semigroups on toric surfaces},
author = {Klaus Altmann and Christian Haase and Alex Küronya and Karin Schaller and Lena Walter},
journal= {arXiv preprint arXiv:2209.06044},
year = {2026}
}
Comments
22 pages, 13 figures