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<p>We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi–Yau manifolds in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}^{n+2}, n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. This gluing theorem verifies a conjecture by Li (Geom Funct Anal 29(4):1002–1047, 2019) 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.</p>

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A gluing theorem for collapsing warped-QAC Calabi–Yau manifolds

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Dashen Yan

摘要

We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi–Yau manifolds in \(\mathbb {C}^{n+2}, n\ge 2\) C n + 2 , n ≥ 2 . This gluing theorem verifies a conjecture by Li (Geom Funct Anal 29(4):1002–1047, 2019) 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.