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Oberseminar WiSe 2008/09 Zusammenfassung des Vortrags von D. Ploog

Homological Mirror Symmetry in the simplest case: elliptic curves

HMS deals with equivalences of triangulated categories of symplectic (A-model) and algebraic (B-model) origin. The first cases to be studied were Calabi-Yau manifolds X, in which the mirror Y is supposed to be Calabi-Yau as well. HMS predicts A-model(X)=B-model(Y) and vice versa. The conjecture is known for dimension 1 (elliptic curves), abelian varieties and the quartic (K3) surface. In this talk, we will explain the elliptic curve case, following the papers by Polichshuk/Zaslow (and Kreussler).