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Abstract: The geometric objects of study in this paper are K3 surfaces which admit apolarization by the unique even unimodular lattice of signature 1,17. Astandard Hodge-theoretic observation about this special class of K3 surfaces isthat their polarized Hodge structures are identical with the polarized Hodgestructures of abelian surfaces that are cartesian products of elliptic curves.Earlier work of the first two authors gives an explicit normal form andconstruction of the moduli space for these surfaces. In the present work, thisnormal form is used to derive Picard-Fuchs differential equations satisfied byperiods of these surfaces. We also investigate the subloci of the moduli spaceon which the polarization is enhanced. In these cases, we derive informationabout the Picard-Fuchs differential equations satisfied by periods of thesesubfamilies, and we relate this information to the theory of genus zeroquotients of the upper half-plane by Moonshine groups. For comparison, we alsoexamine the analogous theory for elliptic curves in Weierstrass form.



Autor: A. Clingher, C.F. Doran, J. Lewis, U. Whitcher

Fuente: https://arxiv.org/







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