Some Remarks on the Wu--Yau Theorem
Differential Geometry
2023-06-21 v2 Algebraic Geometry
Complex Variables
Abstract
The Wu--Yau theorem asserts that a compact K\"ahler manifold with negative holomorphic sectional curvature admits a cohomologous metric with negative Ricci curvature. We introduce a conjectural positive analog of the Wu--Yau theorem and present several examples verifying the conjecture. We also produce an abundance of examples of K\"ahler--Einstein metrics on K\"ahler surfaces of general type that do not have negative holomorphic sectional curvature. This begins to address a question raised by Diverio.
Cite
@article{arxiv.2306.06509,
title = {Some Remarks on the Wu--Yau Theorem},
author = {Kyle Broder},
journal= {arXiv preprint arXiv:2306.06509},
year = {2023}
}
Comments
10 pages; Updated to include some additional details and references