Generic regularity of intermediate complex structure limits

TL;DR

This paper investigates the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds near an intermediate complex structure limit, demonstrating improved convergence results in generic regions.

Contribution

It advances understanding of metric convergence near intermediate limits, refining previous $C^0$-convergence results to metric convergence for collapsing Calabi-Yau metrics.

Findings

Enhanced convergence from $C^0$ to metric in generic regions

Detailed analysis of polarized degenerations of Calabi-Yau manifolds

Improved understanding of geometric limits near intermediate complex structure points

Abstract

We study certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, and improve the potential $C^0$-convergence to a metric convergence result on the generic region for the corresponding collapsing Ricci-flat K\"ahler metrics.