Collapsing hyperkÄhler manifolds

Valentino Tosatti, Yuguang Zhang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)751-786
Number of pages36
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Issue number3
StatePublished - 2020

ASJC Scopus subject areas

  • General Mathematics


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