Browsing by Subject "Sextic curve"
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Item Open Access Smooth models of singular K3-surfaces(European Mathematical Society Publishing House, 2019) Degtyarev, AlexanderWe 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.Item Open Access Tritangents to smooth sextic curves(Association des Annales de l'Institut Fourier, 2022-10-21) Degtyarev, AlexWe prove that a smooth plane sextic curve can have at most 72 tritangents, whereas a smooth real sextic may have at most 66 real tritangents. © 2022 Association des Annales de l'Institut Fourier. All rights reserved.