arXiv subjects
Publications and source records attributed to Laurent Battisti.
In this paper we describe the construction of a new class of non-Kähler compact complex manifolds. They can be seen as a generalization of Sankaran, OT and LVMB manifolds. Moreover, we give properties of these new spaces. Their Kodaira dimension is $-\infty$ and under a mild condition they have algebraic dimension equal to zero.
In this paper we extend results due to Vogt on line bundles over Cousin groups to the case of domains stable by the maximal compact subgroup. This is used in the sequel to show that the algebraic dimension of OT-manifolds is zero. In the last part we establish that certain Cousin groups, in particular those arising from the construction of OT-manifolds, have finite-dimensional irregularity.
In this article, we study a class of manifolds introduced by Bosio called $\LVMB$ manifolds. We provide an interpretation of his construction in terms of quotient of toric manifolds by complex Lie groups. Furthermore, $\LVMB$ manifolds extend a class of manifolds obtained by Meersseman, called $\LVM$ manifolds, and we give a characterization of these manifolds using our toric description. Finally, we give an answer to a question asked by Cupit-Foutou and Zaffran.
Let $S$ be an intermediate Kato surface, $D$ the divisor consisting of all rational curves of $S$, $\widetilde{S}$ the universal covering of $S$ and $\widetilde{D}$ the preimage of $D$ in $\widetilde{S}$. We prove two results about the surface $\widetilde{S}\setminus \widetilde{D}$: it is Stein (which was already known when $S$ is either a Enoki or a Inoue-Hirzebruch surface) and we give a necessary and sufficient condition so that its holomorphic tangent bundle is holomorphically trivialisable. ----- Soient $S$ une surface de Kato intermédiaire, $D$ le diviseur formé des courbes rationnelles de $S$, $\widetilde{S}$ le revêtement universel de $S$ et $\widetilde{D}$ la préimage de $D$ dans $\widetilde{S}$. On donne deux résultats concernant la surface $\widetilde{S}\setminus \widetilde{D}$, à savoir qu'elle est de Stein (ce qui était connu dans le cas où $S$ est une surface d'Enoki ou d'Inoue-Hirzebruch) et on donne une condition nécessaire et suffisante pour que son fibré tangent holomorphe soit holomorphiquement trivialisable.