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- W4297882682 abstract "We consider a multi-parameter family of canonical coordinates and mirror maps o riginally introduced by Zudilin [Math. Notes 71 (2002), 604-616]. This family includes many of the known one-variable mirror maps as special cases, in particular many of modular origin and the celebrated example of Candelas, de la Ossa, Green and Parkes [Nucl. Phys. B359 (1991), 21-74] associated to the quintic hypersurface in $mathbb P^4(mathbb C)$. In [Duke Math. J. 151 (2010), 175-218], we proved that all coeffi cients in the Taylor expansions at 0 of these canonical coordinates (and, hence, of the corresponding mirror maps) are integers. Here we prove that all coefficients in the Taylor expansions at 0 of these canonical coordinates are positive. Furthermore, we provide several results pertaining to the behaviour of the canonical coordinates and mirror maps as complex functions. In particular, we address analytic continuation, points of singularity, and radius of convergence of these functions. We present several very precise conjectures on the radius of convergence of the mirror maps and the sign pattern of the coefficients in their Taylor expansions at 0." @default.
- W4297882682 created "2022-10-01" @default.
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- W4297882682 date "2011-02-25" @default.
- W4297882682 modified "2023-10-18" @default.
- W4297882682 title "Analytic properties of mirror maps" @default.
- W4297882682 doi "https://doi.org/10.48550/arxiv.1102.5375" @default.
- W4297882682 hasPublicationYear "2011" @default.
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