On torus actions of higher complexity
Algebraic Geometry
2021-02-04 v3
Abstract
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of general arrangement varieties and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.
Cite
@article{arxiv.1802.00417,
title = {On torus actions of higher complexity},
author = {Juergen Hausen and Christoff Hische and Milena Wrobel},
journal= {arXiv preprint arXiv:1802.00417},
year = {2021}
}
Comments
Background, examples and references added, more self-contained presentation, 54 pages