Some Remarks on the Wu--Yau Theorem

Author:

Kyle Broder

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-06-09 16:00:00

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.

PDF: Some Remarks on the Wu--Yau Theorem.pdf