Constructions of singular rational surfaces of Picard number one with ample canonical divisor

2010/07/12 by DongSeon Hwang, Hwang, DongSeon, JongHae Keum +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1007.1936

13 pages, 7 figures

arxiv created 2010/07/12 · openalex publication_date 2010/07/12 · arxiv updated 2010/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kollár gave a series of examples of rational surfaces of Picard number 1 with ample canonical divisor having cyclic singularities. In this paper, we construct several series of new examples in a geometric way, i.e., by blowing up several times inside a configuration of curves on the projective plane and then by contracting chains of rational curves. One series of our examples have the same singularities as Kollár's examples.

Citations

• Algebraic Montgomery-Yang Problem: the noncyclic case

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