Work

Some remarks on the uniqueness of the complex projective spaces

Year: 2016

Type: article

Abstract: We first note in this article that if a compact Kähler manifold has the same integral cohomology ring and Pontrjagin classes as the complex projective space C P n , then it is biholomorphic to C P n provided n is odd. The same holds for even n if we further assume that the fundamental group of M is finite. This technically refines a classical result of Hirzebruch–Kodaira and Yau. This observation, together with a result of Dessai and Wilking, enables us to characterize all C P n in terms of homotopy type under some symmetry condition. When n = 4 , we can drop the requirement on Pontrjagin classes by showing that a compact Kähler manifold with finite fundamental group and having the same integral cohomology ring as C P 4 is biholomorphic to C P 4 , which improves on results of Fujita and Libgober–Wood.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms/bdw009

Author: Ping Li

Institution: Tongji University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, National Taiwan University, Fundamental Research Funds for the Central Universities, Division of Mathematical Sciences

Award: 黎曼面上与稳定向量丛相关的若干几何拓扑性质的研究