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arXiv · 1705.03299

Collapsing hyperk\"ahler manifolds

Valentino Tosatti·Yuguang Zhang
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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.

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BibTeXRIS

Valentino Tosatti, Yuguang Zhang. 2017-05-09. Collapsing hyperk\"ahler manifolds. https://doi.org/10.24033/asens.2433

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