Duality between the pseudoeffective and the movable cone on a projective manifold
Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016
Location: SLMath: Eisenbud Auditorium
algebraic geometry and GAGA
mathematical physics
complex differential geometry
Kahler metric
mirror symmetry
projective algebraic manifolds
ample and effective divisors
Kahler cones
51E14 - Finite partial geometries (general), nets, partial spreads
14H60 - Vector bundles on curves and their moduli [See also 14D20, 14F06, 14J60]
14J42 - Holomorphic symplectic varieties, hyper-Kähler varieties
14470
The structure of projective algebraic manifolds is to a large extent governed by the geometry of its cones of divisors or curves. In the case of divisors, two cones are of primary importance: the cone of ample divisors and the cone of effective divisors (and the closure of these cones as well). These cones have natural transcendental analogues on any compact Kähler manifold, namely the cone of Kähler classes (called the Kähler cone) and the cone of pseudoeffective (1,1)-classes (called the pseudoeffective cone).
A conjecture of Boucksom-Demailly-Paun-Peternell says that the pseudoeffective cone is dual to the cone of movable classes. I will discuss my recent proof of the conjecture in the case when the manifold is projective
14470
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