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Holomorphic one-forms
without zeros on threefolds
Feng Hao and Stefan Schreieder |
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Geometry & Topology 25 (2021) 409–444
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Abstract |
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We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real –manifold is a –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
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Mathematical Subject Classification 2010
Primary: 14F45, 14J30, 32Q55
Secondary: 32Q57
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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
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Authors |
| Feng Hao | |
| Mathematisches Institut LMU München München Germany |
KU Leuven Leuven Belgium |
| Stefan Schreieder | |
| Mathematisches Institut LMU München München Germany |
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