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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 4, Pages 167–230 (Mi izv8438)  

This article is cited in 1 scientific paper (total in 1 paper)

A criterion for semiampleness

V. V. Shokurov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: 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: sobor, skrepa, big, colimit, nef, semiampleness.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/im8438

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English version:
Izvestiya: Mathematics, 2017, 81:4, 827–887

Bibliographic databases:

UDC: 512.76
MSC: 14C20, 14E30
Received: 12.08.2015

Citation: V. V. Shokurov, “A criterion for semiampleness”, Izv. RAN. Ser. Mat., 81:4 (2017), 167–230; Izv. Math., 81:4 (2017), 827–887

Citation in format AMSBIB
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\pages 827--887
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  • https://doi.org/10.4213/im8438
  • http://mi.mathnet.ru/eng/izv/v81/i4/p167

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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