A reduction map for nef line bundles
By Thomas Bauer, Frédéric Campana, T. Eckl, Stefan Kebekus, T. Peternell, S. Rams, Tomasz Szemberg, Lorenz Wotzlaw. 2001
100 citations recorded by the source corpus.
In [Ts00], H. Tsuji stated several very interesting assertions on the structure of pseudo-effective line bundles L on a projective manifold X. In particular he postulated the existence of a meromorphic “reduction map”, which essentially says that through the general point of X there is a maximal irreducible L-flat subvariety. Moreover the reduction map should be almost holomorphic, i.e. has compact fibers which do not meet the indeterminacy locus of the reduction map. The proofs of [Ts00], however, are extremely difficult to follow.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/091bfe08f6b3891fd018310dc1b6de86636756f0
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Citations in the corpus
- The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension (2004, background): “So N is contained in fibers of g and Z = f ∗(OY (a)), [ Workshop ,2.11]; moreover a ≥ 0. Comparing with (∗∗) we get Z = f ∗(A) and thus A is nef.”
- Minimal Model Theory for Log Surfaces (2010, background): “Let us quickly recall the reduction map and the nef dimension in [B8].”
- Existence of Mori fibre spaces for 3-folds in char $p$ (2014, background): “The theorem was proved in [1] for k of characteristic 0 and L a Q-divisor.”
- On the canonical line bundle and negative holomorphic sectional curvature (2009, background): “Since it is very difficult to produce a section of mKM solely based on the fact that KM is nef, it is tempting to consider the nef dimension and nef reduction map introduced by Tsuji ([26], see also [5], [6], [2]).”