Holomorphic one-forms without zeros on threefolds

Hao, Feng; Schreieder, Stefan

doi:10.2140/gt.2021.25.409

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Holomorphic one-forms without zeros on threefolds

Feng Hao and Stefan Schreieder

Geometry & Topology 25 (2021) 409–444

DOI: 10.2140/gt.2021.25.409

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

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

Volume 25, issue 1 (2021)