Categorical Mirror Symmetry: The Elliptic Curve

Details Categorical Mirror Symmetry: The Elliptic Curve Categorical Mirror Symmetry: The Elliptic Curve

1998-01-26

arxiv.org/abs/math/9801119v3

Adv.Theor.Math.Phys.2:443-470,1998

Mathematics

Algebraic Geometry

harvmac, 29 pages (big); updated with corrections

Scientific paper

We describe an isomorphism of categories conjectured by Kontsevich. If $M$ and $\widetilde{M}$ are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on $M$ and a suitable version of Fukaya's category of Lagrangian submanifolds on $\widetilde{M}.$ We prove this equivalence when $M$ is an elliptic curve and $\widetilde{M}$ is its dual curve, exhibiting the dictionary in detail.

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