Title: Collapsing hyperkähler manifolds,
Abstract: Given a projective hyperkahler manifold with a holomorphic Lagrangian
fibration, we prove that hyperkahler metrics with volume of the torus fibers
shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away
from the singular fibers) to a compact metric space which is a half-dimensional
special Kahler manifold outside a singular set of real Hausdorff codimension 2
and is homeomorphic to the base projective space.