English

On projectivized vector bundles and positive holomorphic sectional curvature

Differential Geometry 2023-03-31 v1 Algebraic Geometry Complex Variables

Abstract

We generalize a construction of Hitchin to prove that, given any compact K\"ahler manifold MM with positive holomorphic sectional curvature and any holomorphic vector bundle EE over MM, the projectivized vector bundle P(E){\mathbb P}(E) admits a K\"ahler metric with positive holomorphic sectional curvature.

Keywords

Cite

@article{arxiv.1606.08347,
  title  = {On projectivized vector bundles and positive holomorphic sectional curvature},
  author = {Angelynn Alvarez and Gordon Heier and Fangyang Zheng},
  journal= {arXiv preprint arXiv:1606.08347},
  year   = {2023}
}