Holomorphic one-forms without zeros on threefolds
Algebraic Geometry
2021-03-10 v2 Complex Variables
Geometric Topology
Abstract
We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our results prove a conjecture of Kotschick in dimension three.
Cite
@article{arxiv.1906.07606,
title = {Holomorphic one-forms without zeros on threefolds},
author = {Feng Hao and Stefan Schreieder},
journal= {arXiv preprint arXiv:1906.07606},
year = {2021}
}
Comments
32 pages, final version, to appear in Geometry & Topology