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Un résultat sur les faces du cône des 1-cycles effectifs. (A result on the faces of the cone of effective 1-cycles). (French) Zbl 0624.14006
Let X, Y be normal projective varieties and X have canonical singularities. Let \(f: X\to Y\) be a birational map with exceptional set E and L an ample divisor in Y. Suppose that \(-K_ X|_ E\) is numerically positive. Then it is proved here that the closed set Z in the closed convex cone of effective 1-cycles in X satisfying \(K_ X\cdot Z\leq 0\) and \(f^*(L)\cdot Z=0\) is a convex cone with finite number of faces. Like the theorem of Kollár this also is deduced from a bound on the numerator of a numerical invariant.
Reviewer: K.Lai
MSC:
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14C20 Divisors, linear systems, invertible sheaves
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