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Algebraicity of the ample cone of projective varieties. (English) Zbl 0728.14004
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.

14C20 Divisors, linear systems, invertible sheaves
14P05 Real algebraic sets
14C22 Picard groups
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