Families of singular Chern-Ricci flat metrics
Complex Variables
2025-03-04 v2 Differential Geometry
Abstract
We prove uniform a priori estimates for degenerate complex Monge-Amp\`ere equations on a family of hermitian varieties. This generalizes a theorem of Di Nezza-Guedj-Guenancia to hermitian contexts. The main result can be applied to study the uniform boundedness of Chern-Ricci flat potentials in conifold transitions.
Keywords
Cite
@article{arxiv.2112.08993,
title = {Families of singular Chern-Ricci flat metrics},
author = {Chung-Ming Pan},
journal= {arXiv preprint arXiv:2112.08993},
year = {2025}
}
Comments
27 pages; v2: we added a locally irreducible assumption in Theorem A and a remark in section 1.2, corrected a few typos, improved the exposition, and updated the references. To appear in J. Geom. Anal