Edges, Orbifolds, and Seiberg-Witten Theory

2013/05/08 by Claude LeBrun, LeBrun, Claude
Mathematics · #53C21 #53C25 (primary) #57R18 #57R57 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C21 #msc:53C25 #msc:57R18 #msc:57R57

paper · pdf · doi:10.48550/arxiv.1305.1960

54 pages, two figures

arxiv created 2013/05/08 · openalex publication_date 2013/05/08 · arxiv updated 2013/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Seiberg-Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form 2(pi)/p, where p is a positive integer, but we conjecture that similar results will also hold in greater generality.

Citations

• Algebraic surfaces and Seiberg-Witten invariants
• Differential Forms in Algebraic Topology
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Ricci flat Kahler metrics with edge singularities
• A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics

Related

• Einstein Metrics, Four-Manifolds, and Differential Topology
• Weyl Curvature, Einstein Metrics, and Seiberg-Witten Theory
• On the nonexistence of Einstein metric on 4-manifolds
• Curvature and Smooth Topology in Dimension Four
• Constraints on embedded spheres and real projective planes in 4-manifolds from Seiberg-Witten theory