Categorical Mirror Symmetry: The Elliptic Curve

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dc.creatorPolishchuk, Alexander
dc.creatorZaslow, Eric
dc.date1998-01-26
dc.date2000-04-07
dc.date.accessioned2026-07-07T11:36:27Z
dc.date.available2026-07-07T11:36:27Z
dc.descriptionWe 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.
dc.descriptionharvmac, 29 pages (big); updated with corrections
dc.identifierhttps://arxiv.org/abs/math/9801119
dc.identifierhttp://arxiv.org/abs/math/9801119
dc.identifierAdv.Theor.Math.Phys.2:443-470,1998
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198925
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleCategorical Mirror Symmetry: The Elliptic Curve
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