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Mirror symmetry for plane cubics revisited. (English) Zbl 1405.14106
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-363-0/pbk). Advanced Lectures in Mathematics (ALM) 42, 593-619 (2018).
Summary: In this expository note we discuss some arithmetic aspects of the mirror symmetry for plane cubic curves. We also explain how the Picard-Fuchs equation can be used to reveal part of these arithmetic properties. The application of Picard-Fuchs equations in studying the genus zero Gromov-Witten invariants of more general Calabi-Yau varieties and the Weil-Petersson geometry on their moduli spaces will also be discussed.
For the entire collection see [Zbl 1398.14003].

14J33 Mirror symmetry (algebro-geometric aspects)
14H50 Plane and space curves
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