Mirror symmetry for certain non-Kähler elliptic surfaces

Abstract: The logarithmic transformation is an operation on complex elliptic surfaces which can be used to produce interesting spaces from more familiar ones. I will first give homological mirror symmetry results for surfaces which are constructed by performing two logarithmic transformations to the product of P^1 with an elliptic curve, a class of surfaces which includes the classical Hopf surface (S^1 x S^3). I will then use this work, along with work of Auroux, Efimov and Katzarkov on the Fukaya category of singular curves, to describe some work in progress on a potential mirror operation to the logarithmic transformation and some applications.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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