Zeros of holomorphic one-forms and topology of Kähler manifolds

Abstract

A conjecture of Kotschick predicts that a compact Kähler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao, we use our approach to prove Kotschick's conjecture for smooth projective threefolds.

13 pages, with an Appendix written jointly with Hsueh-Yung Lin; final version, to appear in IMRN