G2-manifolds from K3 surfaces with non-symplectic automorphisms

Details G2-manifolds from K3 surfaces with non-symplectic automorphisms G2-manifolds from K3 surfaces with non-symplectic automorphisms

2011-10-12

arxiv.org/abs/1110.2623v3

Mathematics

Differential Geometry

32 pages; v2: A further reference and a new proof for the fact that D is an anti-canonical divisor are added; v3: Some typos c

Scientific paper

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.

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