Geodesic
A criterion for semiampleness
Izvestiya. Mathematics, Tome 81 (2017) no. 4, pp. 827-887 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] V. V. Shokurov, Skrepa morphisms (to appear)

[2] V. V. Shokurov, Log Adjunction: effectiveness and positivity, arXiv: 1308.5160

[3] C. Birkar, The augmented base locus of real divisors over arbitrary fields, arXiv: 1312.0239v1

[4] A. Grothendieck, “Éléments de géoméntrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. IV”, Inst. Hautes Études Sci. Publ. Math., 32 (1967), 5–361 | DOI | MR | Zbl

[5] R. Hartshorne, Algebraic geometry, Grad. Texts in Math., 52, Springer-Verlag, New York–Heidelberg, 1977, xvi+496 pp. | DOI | MR | MR | Zbl | Zbl

[6] S. Keel, “Basepoint freeness for nef and big line bundles in positive characteristic”, Ann. of Math. (2), 149:1 (1999), 253–286 | DOI | MR | Zbl

[7] M. Artin, “Algebraization of formal moduli. II. Existence of modifications”, Ann. of Math. (2), 91 (1970), 88–135 | DOI | MR | Zbl

[8] D. Knutson, Algebraic spaces, Lecture Notes in Math., 203, Springer-Verlag, Berlin-New York, 1971, vi+261 pp. | DOI | MR | Zbl

[9] H. Matsumura, Commutative ring theory, Cambridge Stud. Adv. Math., 8, Cambridge Univ. Press, Cambridge, 1986, xiv+320 pp. | DOI | MR | Zbl