Holomorphic one-forms without zeros on threefolds

Hao, Feng¹ ; Schreieder, Stefan²

¹ Mathematisches Institut, LMU München, München, Germany, KU Leuven, Leuven, Belgium
² Mathematisches Institut, LMU München, München, Germany

Geometry & topology, Tome 25 (2021) no. 1, pp. 409-444.

Résumé

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.

Détail

DOI : 10.2140/gt.2021.25.409

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

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