Generalized Albanese morphisms

2003/04/04 by Georg Hein, Hein, Georg
Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #14D20 #14J10 #Algebraic Geometry (math.AG) #Balkans: History, Politics, Society #Bioactive natural compounds #China's Ethnic Minorities and Relations #FOS: Mathematics #math.AG #msc:14D20 #msc:14J10

paper · pdf · doi:10.48550/arxiv.math/0304057

15 pages, LaTeX, major revision, the paper has been completely rewritten and greatly expanded compared to the previous version

openalex publication_date 2003/04/04 · arxiv created 2004/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define generalizations of the Albanese variety for a projective variety X. The generalized Albanese morphisms X --> Alb_r(X) contract those curves C in X for which the induced morphism Hom(π₁(X),U(r)) --> Hom(π₁(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.

Related

• The Albanese morphism for hyperelliptic varieties
• On varieties of maximal Albanese dimension
• Albanese maps for open algebraic spaces
• Description of generalized Albanese varieties by curves
• On the Albanese map for smooth quasi-projective varieties