ScalingStacks

Remark 1.4 . [03G3]

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Remark 1.4.

The volume of the hyperkähler metrics in Theorem 1.1 is comparable to β−4\beta^{-4}. If one scales these metrics to have unit volume instead of unit diameter, it is not hard to see that the possible pointed Gromov-Hausdorff limits are either 𝕋2×ℝ\mathbb{T}^{2}\times\mathbb{R} or 𝕋2×[0,∞)\mathbb{T}^{2}\times[0,\infty), depending on the basepoint (see Section 7.3). Thus under this scaling, the nilmanifolds disappear and one sees only a simple S1S^{1}-collapse. However, the bubbles remain the same.

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