Smooth models of singular K3-surfaces

Date

2019

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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.

Source Title

Revista Matematica Iberoamericana

Publisher

European Mathematical Society Publishing House

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Published Version (Please cite this version)

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English