Finite generation of certain valuation semigroups on toric surfaces

by Dr Jyoti Dasgupta (TIFR, Mumbai)

Wednesday 22 Feb 2023, 16:00 → 17:00 Asia/Kolkata

AG-77

Abstract: In this talk, we will discuss a preprint of Klaus Altmann, Christian Haase, Alex Kuronya, Karin Schaller, and Lena Walter, available at https://arxiv.org/abs/2209.06044. Finite generation of semigroups or rings arising from geometric situations has been a question of interest for a long time. In this preprint, the authors consider valuation semigroups arising from Newton-Okounkov theory in the special case of toric surfaces. They 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.