The Hodge conjecture for powers of K3 surfaces of Picard number 16

TL;DR

This paper investigates the Hodge conjecture for powers of K3 surfaces, demonstrating that algebraicity of the Kuga--Satake correspondence implies the conjecture for all powers within a specific family.

Contribution

It establishes a conditional link between the algebraicity of the Kuga--Satake correspondence and the Hodge conjecture for powers of K3 surfaces of Picard number 16.

Findings

Hodge conjecture holds for all powers of K3 surfaces if Kuga--Satake correspondence is algebraic.

The result applies to a family of K3 surfaces with generic Picard number 16.

Provides a new approach to verify the Hodge conjecture in this context.

Abstract

We study the Hodge conjecture for powers of K3 surfaces and show that if the Kuga--Satake correspondence is algebraic for a family of K3 surfaces of generic Picard number 16, then the Hodge conjecture holds for all powers of any K3 surface in that family.