2024/11/03 by Yueqing Feng, Feng, Yueqing
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2411.01459
openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a strictly unbounded toric symplectic 4-manifold, we explicitly construct complete toric scalar-flat Kähler metrics on the complement of a toric divisor. These symplectic 4-manifolds correspond to a specific class of non-compact Kähler surfaces. We also provide an alternative construction of toric scalar-flat Kähler metrics with conical singularity along the toric divisor, following the approach of Abreu and Sena-Dias.