1.1.2. Codimension- 1 collapse [03FW]
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1.1.2. Codimension- collapse
In [Fos16] Foscolo constructed a family of hyperkähler metrics on a surface that collapses to the flat orbifold . The collapse has bounded curvature away from finitely many points, and is given by shrinking the fibers of an -fibration. In the simplest case, curvature blow-up occurs at the 8 singular points of , where the bubbles are given by complete hyperkähler spaces with cubic volume growth, which in this case are ALF- spaces. See [CC15, Min11] for a partial classification of hyperkähler ALF spaces. Let us also point out that the results of [Fos16] have motivated the study of codimension- collapse of -manifolds to -dimensional Calabi-Yau manifolds in [FHN17].