Zeros of one-forms and homologically trivial fibrations
Algebraic Geometry
2025-12-24 v2 Differential Geometry
Abstract
We show that a conjecture of Kotschick about one-forms without zeros on compact K\"ahler manifolds follows in the case of simple Albanese torus from a conjecture of Bobadilla and Koll\'ar about homologically trivial fibrations. As an application, we prove Kotschick's conjecture for compact K\"ahler manifolds X whose first betti number is at least 2dim(X)-2 and Albanese torus is simple.
Keywords
Cite
@article{arxiv.2210.05697,
title = {Zeros of one-forms and homologically trivial fibrations},
author = {Stefan Schreieder and Ruijie Yang},
journal= {arXiv preprint arXiv:2210.05697},
year = {2025}
}
Comments
5 pages, final version, to appear in Michigan Mathematical Journal. Comments are welcome!