K3 surfaces with non-symplectic involution and compact G2-manifolds

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• Alexei Kovalev, Cambridge
• Wednesday 23 February 2011, 16:00-17:00
• MR4.

If you have a question about this talk, please contact Ivan Smith.

I will describe a large new class of quasiprojective complex algebraic threefolds and their application to constructing many new examples of compact Ricci-flat 7-manifolds with holonomy G_2, via the connected-sum method. The construction requires gluing two `matching’ pieces, each one being a product of a threefold and a circle. The threefolds are obtained using the theory of K3 surfaces with non-symplectic involution due to Nikulin. The relation will also be explained between algebraic invariants of K3 surfaces and the `geography’ of Betti numbers of the new and some previously known compact G_2-manifolds. Joint work with N.-H. Lee.

This talk is part of the Differential Geometry and Topology Seminar series.

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