Galaxy-model conjecture for minimal non-collapsing bubbles
Galaxy-model conjecture for minimal non-collapsing bubbles
Let 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 . Let be the klt locus of the central fiber . Galaxy-model conjecture. Each connected component of appears as a minimal non-collapsing pointed Gromov--Hausdorff limit of the Calabi--Yau metrics, for some sequence of base points in the general fibers . 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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