ScalingStacks

Theorem 1.1 . [02GH]

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Theorem 1.1.

Every collection of 88 ALF spaces of dihedral type M1,…,M8M_{1},\dots,M_{8} and n≤16n\leq 16 ALF spaces of cyclic type N1,…,NnN_{1},\dots,N_{n} satisfying

∑j=18χ⁡(Mj)+∑i=1nχ⁡(Ni)=24\sum_{j=1}^{8}{\chi(M_{j})}+\sum_{i=1}^{n}{\chi(N_{i})}=24

arises as the collection of “bubbles” forming in a sequence of hyperkähler metrics on the K3 surface which collapse to T3/ℤ2T^{3}/\mathbb{Z}_{2} with bounded curvature away from n+8n+8 points.

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