In 1994 M. Kontsevich conjectured that a proper mathematical formulation of the mirror conjecture is provided by an equivalence between Fukaya’s category of a Calabi–Yau manifold X and the derived category of coherent sheaves of the mirror Calabi–Yau manifold Y.We study the structure of a modified Fukaya category F(X) associated with a K3 surface X, and prove that whenever X is an elliptic K3 surface with a section, the derived category of F(X) is equivalent to a subcategory of the derived category D(Y) of coherent sheaves on the mirror K3 surface Y.
Categorial mirror symmetry for K3 surfaces
BARTOCCI, CLAUDIO;
1999-01-01
Abstract
In 1994 M. Kontsevich conjectured that a proper mathematical formulation of the mirror conjecture is provided by an equivalence between Fukaya’s category of a Calabi–Yau manifold X and the derived category of coherent sheaves of the mirror Calabi–Yau manifold Y.We study the structure of a modified Fukaya category F(X) associated with a K3 surface X, and prove that whenever X is an elliptic K3 surface with a section, the derived category of F(X) is equivalent to a subcategory of the derived category D(Y) of coherent sheaves on the mirror K3 surface Y.
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