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Zeros of Holomorphic One-Forms and Topology of Kähler Manifolds
International Mathematics Research Notices ( IF 0.9 ) Pub Date : 2020-01-08 , DOI: 10.1093/imrn/rnz323
Stefan Schreieder 1
Affiliation  

A conjecture of Kotschick predicts that a compact Kahler 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.

中文翻译:

Kähler 流形的全纯单一形式的零点和拓扑

Kotschick 的一个猜想预测紧凑的 Kahler 流形 $X$ 在圆上平滑地纤维化当且仅当它承认没有零的全纯单形式。在本文中,我们开发了一种方法来解决这个猜想,并在维度 2 中对其进行验证。在与 Hao 的联合论文中,我们使用我们的方法来证明 Kotschick 对平滑投影三重的猜想。
更新日期:2020-01-08
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