Campana, Frédéric; Peternell, Thomas Algebraicity of the ample cone of projective varieties. (English) Zbl 0728.14004 J. Reine Angew. Math. 407, 160-166 (1990). Let X be a projective k-scheme where k is an algebraically closed field and D a real divisor in the closure K of the cone \(N^ 1(X)\otimes_{{\mathbb{Z}}}{\mathbb{R}}\) generated by the classes of ample divisors. The authors show that D is exactly in the boundary of K if there is an irreducible closed subscheme \(Y\subset X\), say of dimension s, such that \(D^ s\cdot Y=0\). This is a “real” version of the Nakai- Moishezon criterion for ampleness of divisors. The method of proof depends on the classical approach used by Kleiman. The second part of the paper deals with a more explicit description of the boundary of K and discusses some examples. Reviewer: S.Kosarew (Saint-Martin-d’Heres) Cited in 1 ReviewCited in 23 Documents MSC: 14C20 Divisors, linear systems, invertible sheaves 14P05 Real algebraic sets 14C22 Picard groups Keywords:real divisor; Nakai-Moishezon criterion for ampleness of divisors PDFBibTeX XMLCite \textit{F. Campana} and \textit{T. Peternell}, J. Reine Angew. Math. 407, 160--166 (1990; Zbl 0728.14004) Full Text: Crelle EuDML