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Homogeneous principal bundles over manifolds with trivial logarithmic tangent bundle | Hassan Azad
; Indranil Biswas
; M. Azeem Khadam
; | Date: |
31 Jul 2019 | Abstract: | Winkelmann considered compact complex manifolds $X$ equipped with a reduced
effective normal crossing divisor $D, subset, X$ such that the logarithmic
tangent bundle $TX(-log D)$ is holomorphically trivial. He characterized them
as pairs $(X,, D)$ admitting a holomorphic action of a complex Lie group
$mathbb G$ satisfying certain conditions cite{Wi1}, cite{Wi2}; this $mathbb
G$ is the connected component, containing the identity element, of the group of
holomorphic automorphisms of $X$ that preserve $D$. We characterize the
homogeneous holomorphic principal $H$--bundles over $X$, where $H$ is a
connected complex Lie group. Our characterization says that the following three
are equivalent:
(1)~ $E_H$ is homogeneous.
(2)~ $E_H$ admits a logarithmic connection singular over $D$.
(3)~ The family of principal $H$--bundles ${g^*E_H}_{gin mathbb G}$ is
infinitesimally rigid at the identity element of the group $mathbb G$. | Source: | arXiv, 1908.0522 | Services: | Forum | Review | PDF | Favorites |
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