Browsing by Subject "Sextic curve"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Smooth models of singular K3-surfaces
    (European Mathematical Society Publishing House, 2019) Degtyarev, Alexander
    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.
  • Thumbnail Image
    ItemOpen Access
    Tritangents to smooth sextic curves
    (Association des Annales de l'Institut Fourier, 2022-10-21) Degtyarev, Alex
    We 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.