2004/08/13 by Janós Kollár, János Kollár, Kollár, János
Mathematics · #32Q20 #53C25 (primary) 14J26 #57S15 (secondary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:14J26 #msc:32Q20 #msc:53C25 #msc:57S15
paper · pdf · doi:10.48550/arxiv.math/0408184
arxiv created 2004/08/13 · openalex publication_date 2004/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified. These results are then used to construct positive Ricci curvature Einstein metrics on these manifolds. The proof has 4 main steps. First, the study of the Leray spectral sequence of the Seifert bundle, based on work of Orlik--Wagreich. Second, the study of log Del Pezzo surfaces. Third, the construction of Kähler--Einstein metrics on Del Pezzo orbifolds using the algebraic existence criterion of Demailly--Kollár. Fourth, the lifting of the Kähler--Einstein metric on the base of a Seifert bundle to an Einstein metric on the total space using the Kobayashi--Boyer--Galicki method.