Moduli spaces of hyperkaehler manifolds and mirror symmetry

Details Moduli spaces of hyperkaehler manifolds and mirror symmetry Moduli spaces of hyperkaehler manifolds and mirror symmetry

2002-10-15

arxiv.org/abs/math/0210219v3

Mathematics

Algebraic Geometry

A section is added in which the Mukai lattice is used to explain better some of the formulae. This is the final version

Scientific paper

These are notes of my lectures given at the school on intersection theory and moduli at the ICTP, Trieste. We construct moduli spaces of K3 surfaces and higherdimensional hyperkaehler manifolds, including moduli spaces of (2,2)-conformal field theories associated to hyperkaehler manifolds, and describe their period domains. Recent results on these manifolds are discussed from the moduli space point of view. The second goal is to present a detailed account of mirror symmetry for K3 surfaces. Arguments due to Aspinwall and Morrison allow one to explain various versions of mirror symmetry (e.g. for lattice polarized or elliptic K3 surfaces) by the same general principle.

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