Translator Disclaimer
June 2020 Canonical threefold singularities with a torus action of complexity one and $k$-empty polytopes
Lukas Braun, Daniel Hättig
Rocky Mountain J. Math. 50(3): 881-939 (June 2020). DOI: 10.1216/rmj.2020.50.881

Abstract

We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold singularities. Our classification relies on lattice point emptiness of certain polytopes with rational vertices. We show that in dimension two, such polytopes are sporadic or are given by Farey sequences. We finally present the Cox ring iteration tree of the classified singularities.

Citation

Download Citation

Lukas Braun. Daniel Hättig. "Canonical threefold singularities with a torus action of complexity one and $k$-empty polytopes." Rocky Mountain J. Math. 50 (3) 881 - 939, June 2020. https://doi.org/10.1216/rmj.2020.50.881

Information

Received: 20 July 2018; Revised: 20 August 2019; Accepted: 4 September 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

zbMATH: 07235587
MathSciNet: MR4132617
Digital Object Identifier: 10.1216/rmj.2020.50.881

Subjects:
Primary: 11B57 , 14B05 , 14R05 , 52B20

Keywords: canonical singularities , Farey sequences , k-empty polytopes , varieties with torus action

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
59 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.50 • No. 3 • June 2020
Back to Top