The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
By S. Boucksom, J. Demailly, Mihai Paun, T. Peternell. 2004
660 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/35b7752988bd7fe0bd458f07c7919878e31e6fc2
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In Applied Mathematics
- Valentino Tosatti
- B. Weinkove
- G. Farkas
- G'abor Sz'ekelyhidi
- Xiaokui Yang
- Chi Li
- T. Peternell
- G. Codogni
In Geometry and Topology
- Valentino Tosatti
- G. Farkas
- B. Weinkove
- Stefan Kebekus
- T. Peternell
- D. Greb
- G'abor Sz'ekelyhidi
- Xiaokui Yang
Citations in the corpus
- Positivity of the CM line bundle for families of K-stable klt Fano varieties (2020, background): “The full conjecture has been proven recently in [22], after the first version of this paper was published.”
- The Monge-Ampère equation for (n − 1)-plurisubharmonic functions on a compact Kähler manifold (2013, background): “In a separate development, there has also been recent interest in balanced metrics [49, 18] (see also [4]) in relation to the cone they define in Hn−1,n−1(M,R).”
- Kähler currents and null loci (2013, neutral): “If X is projective then it is enough to assume that X is not uniruled, using the same argument as above together with the main theorem of [6].”
- Movable curves and semistable sheaves (2014, background): “If X is a manifold, it has been shown in [2] that the movable cone is the closure of the convex cone in N1(X)R generated by curves whose deformations cover a dense subset of X.”