Weyl group of type $E_6$ and K3 surfaces

TL;DR

This paper constructs K3 surfaces using invariants of the Weyl group of type E6, analyzing a specific example with Picard number 20, including its elliptic fibration, Picard lattice, and transcendental lattice.

Contribution

It introduces a novel method of constructing K3 surfaces from Weyl group invariants, providing detailed analysis of a high Picard number example.

Findings

Constructed K3 surfaces from E6 Weyl group invariants.

Detailed description of an example with Picard number 20.

Analysis of elliptic fibration, Picard lattice, and transcendental lattice.

Abstract

Adapting methods of previous papers by A. Sarti and the author, we construct K3 surfaces from invariants of the Weyl group of type $\Erm_6$. We study in details one of these surfaces, which turns out to have Picard number $20$: for this example, we describe an elliptic fibration (and its singular fibers), the Picard lattice and the transcendental lattice.