Geodesic
A criterion for semiampleness
Izvestiya. Mathematics , Tome 81 (2017) no. 4, pp. 827-887.

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We suggest a sufficient condition for the existence of a morphism from a diagram of quasipolarized primary algebraic spaces into a polarized pair. Moreover, we describe diagrams in the category of quasipolarized algebraic spaces such that every finite subdiagram of such a diagram has a morphism into a polarized pair and all fine subdiagrams which are closed under inclusions and under skrepas have a polarized colimit. Such diagrams are called sobors, and their arrows are inclusions and skrepas. The main application is a criterion for the semiampleness of a nef invertible sheaf on a complete algebraic space in terms of a sobor.
Keywords: skrepa, big, nef, semiampleness.
Mots-clés : sobor, colimit 
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V. V. Shokurov. A criterion for semiampleness. Izvestiya. Mathematics , Tome 81 (2017) no. 4, pp. 827-887. http://geodesic.mathdoc.fr/item/IM2_2017_81_4_a5/

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