Abstract
Abstract
A protagonist here is a new-type invariant for type II degenerations of K3 surfaces, which is explicit piecewise linear convex function from the interval with at most
$18$
nonlinear points. Forgetting its actual function behavior, it also classifies the type II degenerations into several combinatorial types, depending on the type of root lattices as appeared in classical examples.
From differential geometric viewpoint, the function is obtained as the density function of the limit measure on the collapsing hyper-Kähler metrics to conjectural segments, as in [HSZ19]. On the way, we also reconstruct a moduli compactification of elliptic K3 surfaces by [AB19], [ABE20], [Brun15] in a more elementary manner, and analyze the cusps more explicitly.
We also interpret the glued hyper-Kähler fibration of [HSVZ18] as a special case from our viewpoint, and discuss other cases, and possible relations with Landau–Ginzburg models in the mirror symmetry context.
Publisher
Cambridge University Press (CUP)
Reference80 articles.
1. Root systems and elliptic curves
2. Gravitational instantons with faster than quadratic curvature decay (III)
3. [Od20b] Odaka, Y. , Degenerated Calabi–Yau varieties with infinite components, moduli compactifications, and limit toroidal structures, preprint, arXiv:2011.12748.
4. [Od20a] Odaka, Y. , Polystable log Calabi–Yau varieties and gravitational instantons, preprint, arXiv:2009.13876.
5. Tropical and non-Archimedean limits of degenerating families of volume forms
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