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arXiv · 1608.06746

Smooth models of singular $K3$-surfaces

Alex Degtyarev
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Abstract

We show that the classical Fermat quartic has exactly three smooth spatial models. As a generalization, we give a classification of smooth spatial (as well as some other) models of singular $K3$-surfaces of small discriminant. As a by-product, we observe a correlation (up to a certain limit) between the discriminant of a singular $K3$-surface and the number of lines in its models. We also construct a $K3$-quartic surface with $52$ lines and singular points, as well as a few other examples with many lines or models.

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Alex Degtyarev. 2016-08-24. Smooth models of singular $K3$-surfaces. https://doi.org/10.4171/rmi%2F1051

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