Universally defined cycles

Universally defined cycles

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Claire Voisin, Universite Pierre et Marie Curie
Fine Hall 314

The Franchetta conjecture (now a theorem) says basically that any line bundle on the universal family of curves of genus at least 2 restricts to a multiple of the canonical bundle on each fiber. We formulate a generalization of this statement for surfaces and provide a characterization of the Chern classes: polynomials in the Chern classes are the only "universally defined'' cycles.