CARTAN GEOMETRIES ON COMPLEX MANIFOLDS OF ALGEBRAIC DIMENSION ZERO

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorph...

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Bibliographic Details
Published in:Épijournal de Géométrie Algébrique
Main Authors: Indranil Biswas, Sorin Dumitrescu, Benjamin McKay
Format: Article
Language:English
Published: Association Epiga 2019-12-01
Subjects:
cartan geometry
almost homogeneous space
algebraic dimension
killing vector field
semistability 2010 mathematics subject classification 53c56
14j60
32l05
[math]mathematics [math]
Online Access:https://epiga.episciences.org/4460/pdf
Description
Summary:We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.
ISSN:2491-6765

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