Given a projective hyperkähler manifold with a holomorphic Lagrangian fibration, we prove that hyperkähler 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 Kähler manifold outside a singular set of real Hausdorff codimension 2, and is homeomorphic to the base projective space.
|Original language||English (US)|
|Number of pages||36|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - 2020|
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