Generalized Albanese morphisms

Details Generalized Albanese morphisms Generalized Albanese morphisms

2003-04-04

arxiv.org/abs/math/0304057v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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