Class VII surfaces with b₂ curves

2002/01/02 by Georges Dloussky, Dloussky, Georges, Karl Oeljeklaus +3
Mathematics · #14J99 #32J15 (Primary) #32M05 #57R30 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.CV #msc:14J99 #msc:32J15 #msc:32M05 #msc:57R30

paper · pdf · doi:10.48550/arxiv.math/0201010

27 pages

arxiv created 2002/01/02 · openalex publication_date 2002/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an affirmative answer to a conjecture of Ma. Kato, namely that every compact complex surface S in Kodaira's class VII₀ with b₂(S) > 0 and b₂(S) rational curves, admits a global spherical shell.

Related

• Gauge theoretical methods in the classification of non-Kaehlerian surfaces
• Instantons and curves on class VII surfaces
• Special birational structures on non-Kähler complex surfaces
• On surfaces of class VII₀⁺ with numerically anticanonical divisor
• Classifying VII₀ surfaces with b₂ = 0 via group theory