Holomorphic projective connections on compact complex threefolds

被引：1
|
作者：
Biswas, Indranil [1 ]
Dumitrescu, Sorin [2 ]
机构：
[1] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Mumbai 400005, India
[2] Univ Cote Azur, CNRS, LJAD, Nice, France
来源：
MATHEMATISCHE ZEITSCHRIFT | 2023年 / 304卷 / 02期
关键词：
Holomorphic projective connection; Transitive killing Lie algebra; Projective threefolds; Shimura curve; Modular family of false elliptic curves; CARTAN GEOMETRIES; MANIFOLDS; THEOREM; FORMS;
D O I：
10.1007/s00209-023-03286-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that a holomorphic projective connection on a complex projective threefold is either flat, or it is a translation invariant holomorphic projective connection on an abelian threefold. In the second case, a generic translation invariant holomorphic affine connection on the abelian variety is not projectively flat. We also prove that a simply connected compact complex threefold with trivial canonical line bundle does not admit any holomorphic projective connection.
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页数：32
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