Zeros of holomorphic one-forms and topology of K\"ahler manifolds

Stefan Schreieder

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arXiv · 1906.07598

Zeros of holomorphic one-forms and topology of K\"ahler manifolds

Stefan Schreieder

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Abstract

A conjecture of Kotschick predicts that a compact K\"ahler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao, we use our approach to prove Kotschick's conjecture for smooth projective threefolds.

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BibTeX RIS

Stefan Schreieder. 2019-06-18. Zeros of holomorphic one-forms and topology of K\"ahler manifolds. https://arxiv.org/abs/1906.07598

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