Smooth models of singular -surfaces

  • Alex Degtyarev

    Bilkent University, Ankara, Turkey
Smooth models of singular $K3$-surfaces cover
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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 -surfaces of small discriminant. As a by-product, we observe a correlation (up to a certain limit) between the discriminant of a singular -surface and the number of lines in its models. We also construct a -quartic surface with 52 lines and singular points, as well as a few other examples with many lines or models.

Cite this article

Alex Degtyarev, Smooth models of singular -surfaces. Rev. Mat. Iberoam. 35 (2019), no. 1, pp. 125–172

DOI 10.4171/RMI/1051