The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
| dc.creator | Boucksom, Sébastien | |
| dc.creator | Demailly, Jean-Pierre | |
| dc.creator | Paun, Mihai | |
| dc.creator | Peternell, Thomas | |
| dc.date | 2004-05-14 | |
| dc.date.accessioned | 2026-07-07T05:08:17Z | |
| dc.date.available | 2026-07-07T05:08:17Z | |
| dc.description | 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 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 covering family, has non negative Kodaira dimension. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405285 | |
| dc.identifier | http://arxiv.org/abs/math/0405285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71199 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C17; 14C30; 32J27 | |
| dc.title | The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension | |
| dc.type | text |