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Abstract des Vortrages von Alessandra Sarti

Pell's equation and automorphisms of Hilb^2(K3)


I will present recent results on the automorphism group of the Hilbert scheme of two points on a generic K3 surface of any polarization. In this case the Picard number of the Hilbert scheme is two, which is the minimal possible. In particular by using ampleness results of Bayer-Macri and a detailed study of the isometries of the Picard lattice, I show the existence of non-natural non-symplectic involutions on some Hilbert scheme, depending on the degree of the polarization. In all the results the solutions of certain Pell's equation play a fundamental role. The results are a joint work with S. Boissière, A. Cattaneo, M. Nieper-Wisskirchen.