Revistes Catalanes amb Accés Obert (RACO)

On the Hodge conjecture for products of certain surfaces

José J. Ramón Marí

Resum


In this paper we prove the Hodge conjecture for all products of surfaces $S_1\times\cdots\times S_n$ with $q(S_i) = 2, p_g(S_i) = 1$. We also prove the Hodge conjecture for arbitrary self-products of a $K3$ surface $X$ such that the field $E = End_{hg}T(X)$ is a $CM$-field.

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