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Abstract des Vortrages von Alexey Basalaev

Mirror symmetry for simple elliptic singularity with a group action

Following the idea of Chiodo and Ruan, mirror symmetry should be understood globally - involving not just one mirror symmetry isomorphism, but a family of Frobenius manifolds (or CohFT's) on the B-side that gives mirror isomorphisms to the A-side for a particular values of the parameter. Such a B-side is constructed as a Frobenius manifold of the hypersurface singularity with the choice of the so-called primitive form of Saito, that varies in a family. Canonical choice of the A-side is a GW-theory of some variety, but it turns out that another choice of the A-side is possible, constructed from the singularity itself and a symmetry group of it. For simple elliptic singularities global mirror symmetry was established by Satake,Takahashi and Milanov,Ruan,Krawitz, Shen.

It was recently conjectured that the full picture of the global mirror symmetry can be "orbifolded" - considered with the group action. This is done easily for the GW-theory, but involves serious problems on the B-side because Saito theory can not be applied anymore.

We will construct the B-side and two mirror isomorphisms for the particular simple elliptic singularity with a particular symmetry group.