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Instantons in complex geometry
March 17, 2011 14:30, Moscow

Morrison's movable cone conjecture for projective irreducible holomorphic symplectic manifolds

Eyal Markman
 Video records: Flash Video 2,936.3 Mb Flash Video 482.8 Mb MP4 482.8 Mb

Abstract: We prove a version of the conjecture in the title as a consequence of the Global Torelli Theorem for irreducible holomorphic symplectic manifolds $X$. Let $\mathrm{Bir}(X)$ be the group of birational automorphisms of $X$. As consequence it is shown that for each non-zero integer d there are only finitely many $\mathrm{Bir}(X)$-orbits of complete linear systems, which contain a reduced and irreducible divisor of Beauville-Bogomolov degree $d$. A variant hold for degree zero as well.