Families of singular Chern-Ricci flat metrics
arXiv:2112.08993 · doi:10.1007/s12220-022-01094-9
Abstract
We prove uniform a priori estimates for degenerate complex Monge-Ampère 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.
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