On the finite generation of valuation semigroups on toric surfaces

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 associate...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-05
Main Authors: Altmann, Klaus, Haase, Christian, Küronya, Alex, Schaller, Karin, Walter, Lena
Format: Article
Language:English
Subjects:
Combinatorial analysis
Semigroups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.06044