English

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!