Effective basepoint-free theorem for semi-log canonical surfaces

2015/09/24 by Osamu Fujino, Fujino, Osamu
Computer Science · Mathematics · #14C20 (Primary) #14E30 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C20 #msc:14E30

paper · pdf · doi:10.48550/arxiv.1509.07268

15 pages, v2: Section 7 is new, v3: minor modifications, v4: revision following referee's comments. arXiv admin note: text overlap with arXiv:1401.4332; text overlap with arXiv:1601.01028 by other authors

openalex publication_date 2015/09/24 · arxiv created 2017/01/18 · arxiv updated 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proposes a Fujita-type freeness conjecture for semi-log canonical pairs. We prove it for curves and surfaces by using the theory of quasi-log schemes and give some effective very ampleness results for stable surfaces and semi-log canonical Fano surfaces. We also prove an effective freeness for log surfaces.

Citations

• Effective base point free theorem for log canonical pairs--Kollár type theorem
• Basepoint-free theorem of Reid--Fukuda type for quasi-log schemes

Related

• Fujita-type freeness for quasi-log canonical threefolds
• Boundedness of ε-log Canonical Complements on Surfaces
• Kollár-type effective freeness for quasi-log canonical pairs
• Minimal model theory for log surfaces in Fujiki's class \mathcal C
• Failure of Boundedness for Generalised Log Canonical Surfaces