Duality between the pseudoeffective and the movable cone on a projective manifold
Artikel i vetenskaplig tidskrift, 2019

We prove a conjecture of Boucksom-Demailly-Păun-Peternell, namely that on a projective manifold X X the cone of pseudoeffective classes in H R 1 , 1 ( X ) H^{1,1}_{\mathbb {R}}(X) is dual to the cone of movable classes in H R n − 1 , n − 1 ( X ) H^{n-1,n-1}_{\mathbb {R}}(X) via the Poincaré pairing. This is done by establishing a conjectured transcendental Morse inequality for the volume of the difference of two nef classes on a projective manifold. As a corollary the movable cone is seen to be equal to the closure of the cone of balanced metrics. In an appendix by Boucksom it is shown that the Morse inequality also implies that the volume function is differentiable on the big cone, and one also gets a characterization of the prime divisors in the non-Kähler locus of a big class via intersection numbers.

Författare

David Witt Nyström

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Sebastien Boucksom

École polytechnique

Journal of the American Mathematical Society

0894-0347 (ISSN) 1088-6834 (eISSN)

Vol. 32 3 675-689

Ämneskategorier

Matematik

DOI

10.1090/jams/922

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Senast uppdaterat

2024-07-05