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Duality between the pseudoeffective and the movable cone on a projective manifold

Kähler Geometry, Einstein Metrics, and Generalizations March 21, 2016 - March 25, 2016

March 24, 2016 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): David Witt Nystrom (Chalmers University of Technology)
Location: MSRI: Simons Auditorium
  • algebraic geometry and GAGA

  • mathematical physics

  • complex differential geometry

  • Kahler metric

  • mirror symmetry

  • projective algebraic manifolds

  • ample and effective divisors

  • Kahler cones

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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

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