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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von U. Schlickewei

K3 surfaces with real multiplication and the Hodge conjecture

In this talk, I will describe the phenomenon of real multiplication on K3 surfaces and its relations to the Hodge conjecture for self-products of K3 surfaces. Building on work of Van Geemen, the endomorphism algebra of the associated Kuga-Satake Abelian variety can be determined. I will show how to apply this to prove the Hodge conjecture for self-products of double covers of P2 ramified along six lines.