Moduli spaces of hyperkaehler manifolds and mirror symmetry

Abstract

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.

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

References in corpus (3)

• String Theory on K3 Surfaces
• A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6
• Mirror Symmetry on Kummer Type K3 Surfaces

Cited by in corpus (8)

• Abelian fibred holomorphic symplectic manifolds
• Instantons, Hypermultiplets and the Heterotic String
• Period- and mirror-maps for the quartic K3
• Special Lagrangian submanifolds of log Calabi-Yau manifolds
• Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers
• Automorphisms and autoequivalences of generic analytic K3 surfaces
• K3 metrics from little string theory
• Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces