Categorical mirror symmetry: The elliptic curve

Alexander Polishchuk; Eric Zaslow

doi:10.4310/ATMP.1998.v2.n2.a9

Categorical mirror symmetry: The elliptic curve

Alexander Polishchuk^*, Eric Zaslow

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

95 Scopus citations

Abstract

We describe an isomorphism of categories conjectured by Kontsevich. If M and 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 M. We prove this equivalence when M is an elliptic curve and M is its dual curve, exhibiting the dictionary in detail.

Original language	English (US)
Pages (from-to)	443-470
Number of pages	28
Journal	Advances in Theoretical and Mathematical Physics
Volume	2
Issue number	2
DOIs	https://doi.org/10.4310/ATMP.1998.v2.n2.a9
State	Published - Mar 1998

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)

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