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Collapsing Ricci-flat metrics on elliptic K3 surfaces
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2021-01-08, DOI: 10.4310/cag.2020.v28.n8.a9
Gao Chen, Jeff Viaclovsky, Ruobing Zhang

For any elliptic K3 surface $\mathfrak{F} : \mathcal{K} \to \mathbb{P}^1$, we construct a family of collapsing Ricci-flat Kähler 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.