2017/05/19 by Yang Li, Li, Yang
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1705.07026
openalex publication_date 2017/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the study of collapsing Calabi-Yau threefolds with a Lefschetz K3 fibration, we construct a complete Calabi-Yau metric on ℂ3 with maximal volume growth, which in the appropriate scale is expected to model the collapsing metric near the nodal point. This new Calabi-Yau metric has singular tangent cone at infinity, and its Riemannian geometry has certain non-standard features near the singularity of the tangent cone ℂ2/ℤ2 × ℂ, which are more typical of adiabatic limit problems. The proof uses an existence result in H-J. Hein's PhD thesis to perturb an asymptotic approximate solution into an actual solution, and the main difficulty lies in correcting the slowly decaying error terms.