Degenerations, Fibrations, Lattices, and Mirror Symmetry

Alan Thompson (Loughborough University)

Tuesday 16th January 13:00-14:00 110

Abstract

I will present a way to extend the notion of a lattice polarisation to the central fibre of a Type II degeneration of K3 surfaces, generalising ideas of Friedman. I will then discuss the mirror scenario, consisting of an elliptically-fibred K3 surface along with a splitting of the base of the fibration, and show that a similar definition can be made in this setting. Finally, I will discuss how mirror symmetry should relate these two pictures, and describe how this should allow us to describe a notion of lattice polarised mirror symmetry for (quasi) del Pezzo/LG model pairs. This work is joint with Luca Giovenzana.

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