#### Volume 25, issue 1 (2021)

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Holomorphic one-forms without zeros on threefolds

### Feng Hao and Stefan Schreieder

Geometry & Topology 25 (2021) 409–444
##### 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 is a ${C}^{\infty }$–fibre bundle 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.

##### Keywords
topology of algebraic varieties, one-forms, minimal model program, classification, generic vanishing, threefolds
##### Mathematical Subject Classification 2010
Primary: 14F45, 14J30, 32Q55
Secondary: 32Q57