Mirror Symmetry of Calabi-Yau Manifolds and Flat Coordinates
Masayuki Noguchi
TL;DR
This paper investigates mirror symmetry of Calabi-Yau manifolds using the Gauss-Manin system, deriving differential equations for the mirror map and periods in specific models, advancing understanding of mirror symmetry's mathematical structure.
Contribution
It introduces differential equations for the mirror map derived from the Gauss-Manin system, extending the analysis to one- and two-parameter Fermat type Calabi-Yau models.
Findings
Derived differential equations for mirror maps.
Applied to specific Fermat type Calabi-Yau models.
Enhanced understanding of mirror symmetry structure.
Abstract
We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the ordinary Picard-Fuchs equations for the periods. These equations are obtained for a class of one-parameter models and a two-parameter model of Fermat type Calabi-Yau manifolds.
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