Picard-Fuchs Uniformization: Modularity of the Mirror Map and Mirror-Moonshine

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dc.creatorDoran, Charles F.
dc.date1998-12-31
dc.date.accessioned2026-07-07T05:27:24Z
dc.date.available2026-07-07T05:27:24Z
dc.descriptionMotivated 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.
dc.descriptionSubmitted to the Proceedings of NATO-ASI and CRM Summer School on the Arithmetic and Geometry of Algebraic Cycles
dc.identifierhttps://arxiv.org/abs/math/9812162
dc.identifierhttp://arxiv.org/abs/math/9812162
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77908
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectNumber Theory
dc.subject14D05, 11F03, 14J32 (Primary); 30F35, 14J28, 83E30 (Secondary)
dc.titlePicard-Fuchs Uniformization: Modularity of the Mirror Map and Mirror-Moonshine
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