Galaxy-model conjecture for minimal non-collapsing bubbles

From papers

Let (X,L)Δ(\mathcal{X},\mathcal{L})\to\Delta be a non-log-terminal semi-log-canonical, locally stable degeneration of polarized log-terminal projective Calabi--Yau varieties, and enhance it to a polarized galaxy model X~\mathbbmk[[tQ]]\widetilde{\mathcal{X}}\to\mathbbm{k}[[t^{\mathbb{Q}}]]. Let X~0klt\widetilde{\mathcal{X}}^{\rm klt}_0 be the klt locus of the central fiber X~0\widetilde{\mathcal{X}}_0. Galaxy-model conjecture. Each connected component of X~0klt\widetilde{\mathcal{X}}^{\rm klt}_0 appears as a minimal non-collapsing pointed Gromov--Hausdorff limit of the Calabi--Yau metrics, for some sequence of base points ptp_t in the general fibers Xt\mathcal{X}_t. This extends the bubbling picture beyond log-terminal central fibers, where ordinary metric limits are expected to collapse; the conjecture identifies connected components of a galaxy model's klt locus as the relevant infinite-diameter bubbles.

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Sources & referencesView supporting material

Primary source

Yuji Odaka, “Algebraic geometry of bubbling Kahler metrics”, arXiv:2406.14518 (2025).

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