English

Mirror Symmetry for Plane Cubics Revisited

Algebraic Geometry 2021-09-21 v2 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1605.07877,
  title  = {Mirror Symmetry for Plane Cubics Revisited},
  author = {Jie Zhou},
  journal= {arXiv preprint arXiv:1605.07877},
  year   = {2021}
}

Comments

Expository note based on a talk given in the workshop "Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds, and Picard-Fuchs Equations" at the Mittag-Leffler Institute in July 2015. version 2: references added