Work

The topology of Kähler manifolds and 1-forms without zeros

Year: 2026

Type: preprint

Abstract: We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In particular, we construct a smooth projective variety for which the Aomoto complex is exact for every nonzero holomorphic one-form and every semisimple local system, although every closed real one-form, and hence every holomorphic one-form, has a zero.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.04314

Authors: Corrêa, Maurício, Kollár, János, Schreieder, Stefan, Wang, Botong

Institution: Leibniz University Hannover

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220684373

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