Transversely holomorphic branched Cartan geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:134

Article

Biswas, Indranil¹  Dumitrescu, Sorin² 

[1] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Bombay 400005, Maharashtra, India

[2] Univ Cote Azur, IJAD, CNRS, Nice, France

关键词: Holomorphic foliation;    Transverse structure;    Cartan geometry;   

DOI  :  10.1016/j.geomphys.2018.08.005

来源: Elsevier

【 摘 要 】

In Biswas and Dumitrescu (2018), we introduced and studied the concept of holomorphic branched Cartan geometry. We define here a foliated version of this notion; this is done in terms of Atiyah bundle. We show that any complex compact manifold of algebraic dimension d admits, away from a closed analytic subset of positive codimension, a non-singular holomorphic foliation of complex codimension d endowed with a transversely flat branched complex projective geometry (equivalently, a CPd-geometry). We also prove that transversely branched holomorphic Cartan geometries on compact complex projective rationally connected varieties and on compact simply connected Calabi-Yau manifolds are always flat (consequently, they are defined by holomorphic maps into homogeneous spaces). (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free