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

We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi-Yau manifolds in ${\text{CC}}^{n+2},n\ge 2$. 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.