Generalized Albanese morphisms
Abstract
Description
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(π_1(X),U(r)) --> Hom(π_1(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.
15 pages, LaTeX, major revision, the paper has been completely rewritten and greatly expanded compared to the previous version
15 pages, LaTeX, major revision, the paper has been completely rewritten and greatly expanded compared to the previous version