Picard-Fuchs Uniformization: Modularity of the Mirror Map and Mirror-Moonshine
Doran, Charles F.
Algebraic Geometry
High Energy Physics - Theory
Number Theory
14D05, 11F03, 14J32 (Primary); 30F35, 14J28, 83E30 (Secondary)
الأصل · EN
Motivated by a conjecture of Lian and Yau concerning the mirror map in string theory, we determine when the mirror map q-series of certain elliptic curve and K3 surface families are Hauptmoduln (genus zero modular functions). Our geometric criterion for modularity characterizes orbifold uniformization properties of their Picard-Fuchs equations, effectively demystifying the mirror-moonshine phenomenon. A longer, more comprehensive treatment of these results will appear shortly.
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