Picard - Fuchs Uniformization : Modularity of the Mirror Map and Mirror - Moonshine
نویسندگان
چکیده
Motivated by a conjecture of Lian and Yau concerning the mirror map in string theory [LY1, ICMP], we determine when the mirror map qseries 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 can be found in [Dor2]. For a detailed look at several explicit examples of this phenomenon, see the article by Verrill and Yui in this volume [VY].
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