The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimensionReport as inadecuate




The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension - Download this document for free, or read online. Document in PDF available to download.

1 IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche 2 IF - Institut Fourier 3 Géométrie IECL - Institut Élie Cartan de Lorraine 4 IRMA - Institut de Recherche Mathématique Avancée 5 Mathematisches Institut Bayreuth

Abstract : We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a duality statement between the cone of pseudo-effective divisors and the cone of - movable curves - , which is obtained from a general theory of movable intersections and approximate Zariski decomposition for closed positive 1, 1-currents. As a corollary, a projective manifold has a pseudo-effective canonical bundle if and only if it is not uniruled. We also prove that a 4-fold with a canonical bundle which is pseudo-effective and of numerical class zero in restriction to curves of a good covering family, has non-negative Kodaira dimension.





Author: Sébastien Boucksom - Jean-Pierre Demailly - Mihai Paun - Thomas Peternell -

Source: https://hal.archives-ouvertes.fr/



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