Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen type

Abstract

We provide a moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics via compactification of moduli varieties of Morgan-Shalen and Satake type. In patricular, we use it to study the Gromov-Hausdorff limits of hyperKahler metrics with fixed diameters, especially for K3 surfaces.

arXiv commentv2: 184 pages. Published as MSJ Memoir vol.40 (minor revision after v1)