Examples of $K3$ surfaces with real multiplication

Abstract

We construct explicit examples of $K3$ surfaces over $\mathbb{Q}$ having real multiplication. Our examples are of geometric Picard rank 16. The standard method for the computation of the Picard rank provably fails for the surfaces constructed.

References in corpus (2)

• The Tate conjecture for K3 surfaces over finite fields
• K3 surfaces and equations for Hilbert modular surfaces

Cited by in corpus (3)

• Deep Learning Gauss-Manin Connections
• Effective obstruction to lifting Tate classes from positive characteristic
• On families of K3 surfaces with real multiplication