Collapsing K3 Surfaces, Tropical Geometry and Moduli Compactifications of Satake, Morgan-Shalen Type
Yuji Odaka, Yoshiki Oshima
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.
Topics & Concepts
ModuliCompactification (mathematics)MathematicsType (biology)Pure mathematicsModuli spaceGeometryPhysicsGeologyQuantum mechanicsPaleontologyGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory