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Abstract Laterveer

The generalized Franchetta conjecture for hyperkaehler varieties

The generalized Franchetta conjecture as formulated by O’Grady is about algebraic cycles on the universal K3 surface. It is natural to consider a similar conjecture for algebraic cycles on universal families of hyperkaehler varieties. This has close ties to Beauville’s conjectural ``splitting property’’, and the Beauville-Voisin conjecture (stating that the Chow ring of a hyperkaehler variety has a certain subring injecting into cohomology). In my talk, I will attempt to give an overview of these conjectures, and present some cases where they can be proven. This is joint work with Lie Fu, Charles Vial and Mingmin Shen.