Logarithmic Cartan geometry on complex manifolds with trivial logarithmic tangent bundle

Autor:	Biswas, Indranil, Dumitrescu, Sorin, Morye, Archana S.
Rok vydání:	2024
Předmět:	Mathematics - Complex Variables Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Let $M$ be a compact complex manifold, and $D\, \subset\, M$ a reduced normal crossing divisor on it, such that the logarithmic tangent bundle $TM(-\log D)$ is holomorphically trivial. Let ${\mathbb A}$ denote the maximal connected subgroup of the group of all holomorphic automorphisms of $M$ that preserve the divisor $D$. Take a holomorphic Cartan geometry $(E_H,\,\Theta)$ of type $(G,\, H)$ on $M$, where $H\, \subset\, G$ are complex Lie groups. We prove that $(E_H,\,\Theta)$ is isomorphic to $(\rho^* E_H,\,\rho^* \Theta)$ for every $\rho\, \in\, \mathbb A$ if and only if the principal $H$--bundle $E_H$ admits a logarithmic connection $\Delta$ singular on $D$ such that $\Theta$ is preserved by the connection $\Delta$. Comment: Final version to appear in Journal of Differential Geometry and its Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.08593 Zobrazit plný text záznamu View this record from Arxiv