2013/07/10 by Dmitri Bykov, Bykov, Dmitri
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1307.2816
openalex publication_date 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
After a review of the general properties of holomorphic spheres in complex surfaces we describe the local geometry in the vicinity of a CP1 embedded with a negative normal bundle. As a by-product, we build (asymptotically locally hyperbolic) Kahler-Einstein metrics on the total spaces of the line bundles O(-m), m >= 3 over CP1. We check that the behavior of the Kahler potential is compatible with the Chern-Weil formulas for the Euler characteristic and signature. We also describe two supersymmetric setups where relevant constructions arise.