2008/01/20 by DongSeon Hwang, Dongseon Hwang, Hwang, Dongseon +2
Mathematics · #14J17 #14J28 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14J17 #msc:14J28
paper · pdf · doi:10.48550/arxiv.0801.3021
23 pages. changed the exposition of the previous version
openalex publication_date 2008/01/20 · arxiv created 2008/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A normal projective complex surface is called a rational homology projective plane if it has the same Betti numbers with the complex projective plane ℂℙ2. It is known that a rational homology projective plane with quotient singularities has at most 5 singular points. So far all known examples have at most 4 singular points. In this paper, we prove that a rational homology projective plane S with quotient singularities such that KS is nef has at most 4 singular points except one case. The exceptional case comes from Enriques surfaces with a configuration of 9 smooth rational curves whose Dynkin diagram is of type 3A1 ⊕ 2A3. We also obtain a similar result in the differentiable case and in the symplectic case under certain assumptions which all hold in the algebraic case.