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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–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.

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Keywords
topology of algebraic varieties, one-forms, minimal model program, classification, generic vanishing, threefolds
Mathematical Subject Classification 2010
Primary: 14F45, 14J30, 32Q55
Secondary: 32Q57
References
Publication
Received: 1 July 2019
Revised: 27 December 2019
Accepted: 12 February 2020
Published: 2 March 2021
Proposed: Richard P Thomas
Seconded: Dan Abramovich, Ian Agol
Authors
Feng Hao
Mathematisches Institut
LMU München
München
Germany
KU Leuven
Leuven
Belgium
Stefan Schreieder
Mathematisches Institut
LMU München
München
Germany