Closed Meromorphic 1-Forms

Jorge Vitório Pereira ()
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Jorge Vitório Pereira: IMPA

Chapter Chapter 9 in Handbook of Geometry and Topology of Singularities V: Foliations, 2024, pp 447-499 from Springer

Abstract: Abstract We review properties of closed meromorphic 1-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, existence of separatrices, and resolution of singularities under the lenses of the theory of closed meromorphic 1-forms and flat meromorphic connections. We apply the theory to investigate the algebraicity of separatrices in a semi-global setting (neighborhood of a compact curve contained in the singular set of the foliation), and the geometry of smooth hypersurfaces with numerically trivial normal bundle on compact Kähler manifolds.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-52481-3_9

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DOI: 10.1007/978-3-031-52481-3_9

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