Categorical Mirror Symmetry: The Elliptic Curve
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- January 1998
- DOI:
- 10.48550/arXiv.math/9801119
- arXiv:
- arXiv:math/9801119
- Bibcode:
- 1998math......1119P
- Keywords:
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- Algebraic Geometry
- E-Print:
- harvmac, 29 pages (big)