Categorical mirror symmetry: The elliptic curve

Alexander Polishchuk*, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)443-470
Number of pages28
JournalAdvances in Theoretical and Mathematical Physics
Volume2
Issue number2
DOIs
StatePublished - Mar 1998

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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