Generalized Albanese morphisms
arXiv:math/0304057
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(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