Log surfaces of Picard rank one from four lines in the plane

2019/01/31 by Valery Alexeev, Alexeev, Valery, Wenfei Liu +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1902.00102

openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blowups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and the smallest accumulation point of volumes of log canonical surfaces obtained in this way.

Related

• Del Pezzo surfaces with four log terminal singularities
• The maximal number of singular points on log del Pezzo surfaces
• Open surfaces of small volume
• On rank one log del Pezzo surfaces in characteristic different from two and three
• The minimal volume of log surfaces of general type with positive geometric genus