Smooth projective varieties with a torus action of complexity 1 and Picard number 2
Algebraic Geometry
2025-07-08 v3
Abstract
We give an explicit description of all smooth varieties with a torus action of complexity one having Picard number at most two. As a consequence, we classify in every dimension the smooth (almost) Fano varieties with a torus action of complexity one having Picard number two. It turns out that all the Fano examples are obtained via an iterated generalized cone construction from a series of smooth varieties of dimension at most seven.
Keywords
Cite
@article{arxiv.1602.04360,
title = {Smooth projective varieties with a torus action of complexity 1 and Picard number 2},
author = {Anne Fahrner and Juergen Hausen and Michele Nicolussi},
journal= {arXiv preprint arXiv:1602.04360},
year = {2025}
}
Comments
31 pages, new results added