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Collapsing Ricci-flat metrics on elliptic K3 surfaces

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arxiv 1910.11321 v1 pith:KXYU2EZE submitted 2019-10-24 math.DG math.AG

classification math.DGmath.AG
keywords collapsingsingularellipticfibersmathbbmetricmetricsricci-flat
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abstract

For any elliptic K3 surface $\mathfrak{F}: \mathcal{K} \rightarrow \mathbb{P}^1$, we construct a family of collapsing Ricci-flat K\"ahler metrics such that curvatures are uniformly bounded away from singular fibers, and which Gromov-Hausdorff limit to $\mathbb{P}^1$ equipped with the McLean metric. There are well-known examples of this type of collapsing, but the key point of our construction is that we can additionally give a precise description of the metric degeneration near each type of singular fiber, without any restriction on the types of singular fibers.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hyper-K\"ahler manifolds from Riemann-Hilbert problems I: Ooguri-Vafa-like model geometries

    math.DG 2025-01 conditional novelty 6.0 of 10

    The authors rigorously build local hyper-Kähler model geometries, generalizing Ooguri-Vafa and multi-Ooguri-Vafa examples, from the Gaiotto-Moore-Neitzke Riemann-Hilbert formalism.

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