The Hodge conjecture for self-products of certain K3 surfaces

2009/07/15 by Schlickewei, Ulrich
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0907.2503

Abstract

We use a result of van Geemen to determine the endomorphism algebra of the Kuga--Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of \PP² which are ramified along six lines.

Related

• On the Hodge conjecture for products of certain surfaces
• Real multiplication on K3 surfaces and Kuga Satake varieties
• Counterexample to the Hodge Conjecture
• The Hodge standard conjecture for self-products of K3 surfaces
• Kuga-Satake varieties and the Hodge conjecture