Second-order estimates for collapsed limits of Ricci-flat K\"ahler metrics
Differential Geometry
2022-09-14 v3 Complex Variables
Abstract
We show that the singularities of the twisted K\"ahler--Einstein metric arising as the long-time solution of the K\"ahler--Ricci flow or in the collapsed limit of Ricci-flat K\"ahler metrics is intimately related to the holomorphic sectional curvature of the reference conical geometry. This provides an alternative proof of the second-order estimate obtained by Gross--Tosatti--Zhang with explicit constants appearing in the divisorial pole.
Keywords
Cite
@article{arxiv.2106.13343,
title = {Second-order estimates for collapsed limits of Ricci-flat K\"ahler metrics},
author = {Kyle Broder},
journal= {arXiv preprint arXiv:2106.13343},
year = {2022}
}
Comments
16 pages, correction of mistakes in the previous version, comments are welcome