Algebraic Geometry Seminar

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On the Boundedness of the Second Betti Number of Hyperkähler Manifolds

Speaker: Nikon Kurnosov, Higher School of Economics, Moscow

Location: Warren Weaver Hall 201

Date: Tuesday, February 2, 2016, 3:30 p.m.

Synopsis:

An important conjecture of Beauville states that there exists only a finite number of simple hyperkähler manifolds in each dimension up to deformation. Guan has proved it in dimension four. In this talk I will speak on generalizations of his results obtained in recent works of Sawon and myself. In particular, I will explain boundedness conditions for the second Betti number which follow from Rozansky-Witten invariants and an so(4, b_2-2)-action on the cohomology of hyperkähler manifolds.