2009/04/20 by JongHae Keum, Keum, JongHae, DongSeon Hwang +1 · 1 citation
Mathematics · #14J17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0904.2975
openalex publication_date 2009/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Montgomery-Yang problem predicts that every pseudofree differentiable circle action on the 5-dimensional sphere \mathbb S5 has at most 3 non-free orbits. Using a certain one-to-one correspondence, Kollár formulated the algebraic version of the Montgomery-Yang problem: every projective surface S with quotient singularities such that b2(S) = 1 has at most 3 singular points if its smooth locus S0 is simply-connected. In this paper, we prove the conjecture under the assumption that S has at least one noncyclic singularity. In the course of the proof, we classify projective surfaces S with quotient singularities such that (i) b2(S) = 1, (ii) H1(S0, ℤ) = 0, and (iii) S has 4 or more singular points, not all cyclic, and prove that all such surfaces have π1(S0)≅ \mathfrakA5, the icosahedral group.