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Algebraic Geometry Seminar: Misha Verbitsky (HSE Moscow and IMPA, Rio de Janeiro)

Boyd Room 304

Title of talk: Eigenvalues of automorphisms of hyperkahler manifolds

Abstract: Let T be a complex automorphism of a hyperkahler manifold M acting on the second cohomology with an eigenvalue $a^2>1$ (such an automorphism is called hyperbolic, or loxodromic). I would show that all eigenvalues of T on cohomology of M are equal in absolute value to integer powers of a, and the eigenspaces corresponding to the eigenvalue $a^{p-q}$ have the same dimension as $H^{p,q}(M)$. This is a result from a joint work with Bogomolov, Kamenova, Lu.

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