Divisorial properties and special metrics on hypercomplex twistor spaces
Algebraic Geometry
2024-10-28 v1 Complex Variables
Differential Geometry
Abstract
We prove that the general fiber of a compact hypercomplex twistor space with a K\"{a}hler fiber has no divisors nor curves. This is first used to prove that, under the same assumption, the trascendental degree of the field of meromoprhic functions is one. The same result allows to prove that these spaces admit no K\"{a}hler and not even pluriclosed metrics.
Cite
@article{arxiv.2410.19490,
title = {Divisorial properties and special metrics on hypercomplex twistor spaces},
author = {Alberto Pipitone Federico},
journal= {arXiv preprint arXiv:2410.19490},
year = {2024}
}