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

Abstract

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

References in corpus (2)

• A lecture on Kac--Moody Lie algebras of the arithmetic type
• Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

Cited by in corpus (3)

• Algebras, BPS States, and Strings
• Borcherds symmetries in M-theory
• Counting Curves with Modular Forms