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Generalized Albanese morphisms

Georg Hein
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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.

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Georg Hein. 2004-09-27. Generalized Albanese morphisms. https://arxiv.org/abs/math/0304057

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