A review of Lacini's classification of rank one log del Pezzo surfaces in characteristic different from two and three

2025/12/13 by Masaru Nagaoka, Nagaoka, Masaru
Mathematics · #14G17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #Primary 14J26 #Secondary 14J45

paper · pdf · doi:10.48550/arxiv.2512.12294

openalex publication_date 2025/12/13 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

This paper reviews Lacini's classification [Lac24] of log del Pezzo surfaces of rank one in characteristics different from two and three, with a focus on where and how Lacini enhanced the techniques of Keel and McKernan [KM99]. We point out that there is at most one log del Pezzo surface that may have been erroneously omitted from the list in [Lac24, §6.1], namely the surface in Example 3.13. We also extend the results of [Lac24 §4.2] to arbitrary characteristic.

Citations

• Non-log liftable log del Pezzo surfaces of rank one in characteristic five
• On rank one log del Pezzo surfaces in characteristic different from two and three
• Rational Curves on Quasi-Projective Surfaces

Related

• Log del Pezzo Surfaces of Rank 2 and Cartier Index 3 with a Unique Singularity
• On rank one log del Pezzo surfaces in characteristic different from two and three
• Del Pezzo surfaces with four log terminal singularities
• Classification of log del Pezzo surfaces of index three
• Classification of del Pezzo surfaces of rank one. I. Height 1 and 2. II. Descendants with elliptic boundaries