K3 surfaces, Lorentzian Kac--Moody algebras and Mirror Symmetry

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We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the moduli of the mirror family. Lorentzian Kac--Moody algebras are involved in this construction. We give several examples when this conjecture is valid.
15 pages, no figures, AMS-TeX

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