On positive semi-definite holomorphic sectional curvature with many zeroes
Differential Geometry
2023-08-25 v1 Algebraic Geometry
Complex Variables
Abstract
We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane to produce such metrics on the total space of powers of the tautological line bundles over the projective line. We formulate a general conjecture regarding the compact case and use a product approach to obtain an analogous result in the non-compact case.
Keywords
Cite
@article{arxiv.2308.12555,
title = {On positive semi-definite holomorphic sectional curvature with many zeroes},
author = {Minzi Chen and Gordon Heier},
journal= {arXiv preprint arXiv:2308.12555},
year = {2023}
}