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Global smoothings of degenerate K3 surfaces with triple points

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arxiv 2004.03162 v2 pith:NNLTCI6N submitted 2020-04-07 math.DG math.AG

Naoto Yotsutani This is my paper · ORCID
classification math.DGmath.AG
keywords pointssmoothingssurfacestripleahlerianalgebraiccasecompact
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abstract

Let $X$ be a normal crossing compact complex surface with triple points. We prove that there exists a family of smoothings of $X$ when $X$ satisfies suitable conditions. Since our differential geometric proof also includes the case where $X$ is neither K\"ahlerian nor $H^1(X, \mathcal O_X)=0$, this generalizes Friedman's result on degenerations of $K3$ surfaces in algebraic geometry.

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Cited by 1 Pith paper

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  1. Smoothing toroidal crossing spaces

    math.AG 2019-08 conditional novelty 8.0 of 10

    A proof that toroidal crossing spaces with a simple logarithmic section and a transverse anticanonical divisor admit smoothings, together with a proof of Danilov's Hodge-de Rham degeneration conjecture.

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