Year: 2018
Type: preprint
Abstract: Kodaira embedding theorem provides an effective characterization of projectivity of a Kähler manifold in terms the second cohomology. Recently X. Yang [21] proved that any compact Kähler manifold with positive holomorphic sectional curvature must be projective. This gives a metric criterion of the projectivity in terms of its curvature. In this note, we prove that any compact Kähler manifold with positive 2nd scalar curvature (which is the average of holomorphic sectional curvature over 2-dimensional subspaces of the tangent space) must be projective. In view of generic 2-tori being non-abelian, this new curvature characterization is sharp in certain sense.
Source: arXiv (Cornell University)
Authors: Ni, Lei, Zheng, Fangyang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4311346644