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Mathematics > Algebraic Geometry

arXiv:1805.01724 (math)
[Submitted on 4 May 2018]

Title:Collapsing K3 Surfaces and Moduli Compactification

Authors:Yuji Odaka, Yoshiki Oshima
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Abstract:This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to discuss their Gromov-Hausdorff limits along any sequences, which are even not necessarily "maximally degenerating". Our results also give a proof of Kontsevich-Soibelman [KS04, Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.
Comments: 12 pages
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)
Cite as: arXiv:1805.01724 [math.AG]
  (or arXiv:1805.01724v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.01724

Submission history

From: Yuji Odaka [view email]
[v1] Fri, 4 May 2018 11:50:30 UTC (13 KB)
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