Volumes on Complex Analytic Spaces

2013/05/02 by Steven Dale Cutkosky, Cutkosky, Steven Dale
Mathematics · #14C40 #32C35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14C40 #msc:32C35

paper · pdf · doi:10.48550/arxiv.1305.0595

11 pages. arXiv admin note: substantial text overlap with arXiv:1301.5613

arxiv created 2013/05/02 · openalex publication_date 2013/05/02 · arxiv updated 2013/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that volumes and related limits in terms of the Kodaira-Iitaka dimension exist for line bundles and graded linear series on compact reduced complex analytic spaces.

Citations

• The asymptotic growth of graded linear series on arbitrary projective schemes
• Multiplicities of graded families of linear series and ideals
• Multiplicities Associated to Graded Families of Ideals

Related

• Volumes of line bundles
• Kodaira dimension of algebraic fiber spaces over abelian varieties
• Volume functions of linear series
• On the volume of a line bundle
• Kodaira dimension of algebraic fiber spaces over surfaces