G2-manifolds from K3 surfaces with non-symplectic automorphisms

TL;DR

This paper introduces a novel method for constructing compact G2-manifolds using K3 surfaces with non-symplectic automorphisms of prime order, expanding the toolkit for G2-geometry.

Contribution

It extends previous work on involutions to automorphisms of prime order and employs Chen-Ruan orbifold cohomology to analyze the resulting complex threefolds.

Findings

New G2-manifolds constructed from K3 surfaces

Hodge diamonds of complex threefolds determined

Method generalizes previous involution-based approaches

Abstract

We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain complex threefolds, which are the building blocks for this approach.