On the basepoint-free theorem for log canonical threefolds over the algebraic closure of a finite field

2014/07/31 by Diletta Martinelli, Yusuke Nakamura, Jakub Witaszek
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic closure #Algebraic number #Base (topology) #Closure (psychology) #Discrete mathematics #Field (mathematics) #Finite field #Geometry #Mathematical analysis #Mathematics #Point (geometry) #Polynomial and algebraic computation #Pure mathematics #math.AG

paper · pdf · doi:10.2140/ant.2015.9.725

published as Algebra Number Theory 9 (2015) 725-747 · 20 pages. This is the final version, incorporating the referee's suggestions

openalex publication_date 2015/04/17 · arxiv created 2015/05/24 · arxiv updated 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove the basepoint-free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field. This theorem is not valid for any other algebraically closed field.

Citations

• Singularities of the Minimal Model Program
• Birational Geometry of Algebraic Varieties
• On base point free theorem of threefolds in positive characteristic
• Vector Bundles Over an Elliptic Curve
• Enriques' classification of surfaces in char.p, III
• Enriques' Classification of Surfaces in Char. p , II
• Algebraic Geometry
• The Arithmetic of Elliptic Curves