2011/03/05 by Brian Lehmann, Lehmann, Brian
Computer Science · Mathematics · #14C20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Divisor (algebraic geometry) #FOS: Mathematics #Geometry #Mathematics #Polynomial and algebraic computation #Pure mathematics #Quotient #Reduction (mathematics) #Statistics #Variety (cybernetics) #math.AG #msc:14C20
paper · pdf · doi:10.48550/arxiv.1103.1073
26 pages, v3: small revisions in introduction
openalex publication_date 2011/03/05 · arxiv created 2011/09/21 · arxiv updated 2011/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction map and the pseudo-effective reduction map of [Eckl05]. We show that these maps capture interesting geometric properties of L and use them to analyze abundant divisors.