A Gluing Theorem For Collapsing Warped-QAC Calabi-Yau Manifolds

TL;DR

This paper develops a gluing theorem for collapsing warped-QAC Calabi-Yau manifolds, confirming a conjecture about their metric behavior during fiber separation and exploring their bubble tree structure.

Contribution

It introduces a new gluing construction for warped-QAC Calabi-Yau manifolds and verifies a conjecture on their metric collapse behavior.

Findings

Verification of Li's conjecture on metric behavior

Construction of bubble tree structures for collapsing manifolds

Extension of gluing techniques to warped-QAC Calabi-Yau settings

Abstract

We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi-Yau manifolds in $\CC^{n+2}, n\geq 2$. This gluing theorem verifies a conjecture by Yang Li in \cite{li2019gluing} on the behavior of the warped QAC Calabi-Yau metrics on affine quadrics when two singular fibers of a holomorphic fibration go apart. We will also discuss a bubble tree structure for those collapsing warped-QAC Calabi-Yau manifolds.