On the finite generation of valuation semigroups on toric surfaces
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- 10.48550/arXiv.2209.06044
- arXiv:
- arXiv:2209.06044
- Bibcode:
- 2022arXiv220906044A
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14C20;
- 14M25;
- 52B20
- E-Print:
- 22 pages, 13 figures