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September 2021 Noncommutative homological mirror symmetry of elliptic curves
Sangwook Lee
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Kyoto J. Math. 61(3): 723-743 (September 2021). DOI: 10.1215/21562261-2020-0001

Abstract

We prove an equivalence of two A-functors, via Orlov’s Landau–Ginzburg/ Calabi–Yau (LG/CY) correspondence. One is the Polishchuk–Zaslow mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of T2 to a category of noncommutative matrix factorizations. As a corollary, we prove that the noncommutative mirror functor LMgrLt realizes homological mirror symmetry for any t.

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Sangwook Lee. "Noncommutative homological mirror symmetry of elliptic curves." Kyoto J. Math. 61 (3) 723 - 743, September 2021. https://doi.org/10.1215/21562261-2020-0001

Information

Received: 9 May 2018; Revised: 21 March 2019; Accepted: 4 April 2019; Published: September 2021
First available in Project Euclid: 25 May 2021

Digital Object Identifier: 10.1215/21562261-2020-0001

Subjects:
Primary: 53D37
Secondary: 14A22

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 3 • September 2021
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