On the Hodge conjecture for products of certain surfaces

2005/05/17 by Ramón-Marí, José J.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0505357

Abstract

In this paper we prove the Hodge conjecture for products of the form S₁ × ... S_n, where S_i are smooth projective surfaces such that p_g(S_i)=1, q(S_i)=2. We also prove the Hodge conjecture for arbitrary self-products of a K3 surface X such that End_hodge(T(X)) is a CM number field.

Related

• The Hodge standard conjecture for self-products of K3 surfaces
• The Hodge conjecture for self-products of certain K3 surfaces
• Counterexample to the Hodge Conjecture
• Indecomposable K₁ and the Hodge-D-conjecture for K3 and Abelian Surfaces
• The Hodge conjecture for powers of K3 surfaces of Picard number 16