Symplectic automorphisms of Fano varieties of cubic fourfolds and its action on algebraic cycles
Lie Fu (ENS Paris)  Seminar Algebraic Geometry (SAG)
What 


When 
Oct 24, 2013 from 10:30 am to 11:30 am 
Where  Bonn, Hörsaal MPI, Vivatsgasse 7 
Contact Name  sachinidis 
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Abstract: This talk is mainly on the Chowtheoretical aspects of projective
hyperKähler varieties. A smooth projective complex variety is called hyperKähler
if it is simplyconnected and has a unique, up to scalar, holomorphic symplectic
2form. Given a finiteorder symplectic automorphism of such a variety, some
generalization of Bloch's conjecture predicts that the induced action on its Chow
group of zerodimensional cycles is trivial. We prove this conjecture for the Fano
variety of lines of a smooth cubic fourfold (which is a hyperKähler variety by
BeauvilleDonagi's result) under the extra condition that the automorphism
preserves the Plücker polarization. This result partially generalizes a recent
theorem of Huybrechts and Voisin in the case of projective K3 surfaces. If time
permits, some related classification results will also be touched upon.
References: arXiv:1302.6531, arXiv:1303.2241