Collapsing hyperkÄhler manifolds

Valentino Tosatti, Yuguang Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume53
Issue number3
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Collapsing hyperkÄhler manifolds'. Together they form a unique fingerprint.

Cite this