G2-manifolds from K3 surfaces with non-symplectic automorphisms

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.

This paper has been withdrawn since a necessary condition for the existence of an asymptotically cylindrical Calabi-Yau metric on W_1 is in fact not satisified

References in corpus (2)

• K3 surfaces with non-symplectic involution and compact irreducible G_2-manifolds
• Classification of non-symplectic automorphisms of order 3 on $K3$ surfaces