Preprint No. A-03-03

Georg Hein

Generalized Albanese morphisms

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(\pi_1(X),U(r)) --> Hom(\pi_1(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.

Keywords: Moduli spaces, vector bundles, Albanese variety, algebraic surfaces, fundamental group, Shafarevich morphism

Mathematics Subject Classification (MSC2000): 14D20, 14E05

Language: ENG


Contact: Georg Hein, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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