Now showing items 1-6 of 6

    • 800 conics on a smooth quartic surface 

      Degtyarev, Alex (Elsevier BV * North-Holland, 2022-03-10)
      We construct an example of a smooth spatial quartic surface that contains 800 irreducible conics. © 2022 Elsevier B.V.
    • Deformation classes of singular quartic surfaces 

      Aktaş, Çisem Güneş (Bilkent University, 2016-12)
      We study complex spatial quartic surfaces with simple singularities and give their classication up to equisingular deformation. Simple quartics are K3-surfaces and as such they can be studied by means of the global Torelli ...
    • Lines in supersingular quartics 

      Degtyarev, Alex (Nihon Sugakkai,Mathematical Society of Japan, 2021-10-19)
      We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic ...
    • Lines on smooth polarized K3-surfaces 

      Degtyarev, Alex (Springer, 2019)
      For each integer D⩾3D⩾3, we give a sharp bound on the number of lines contained in a smooth complex 2D-polarized K3-surface in PD+1PD+1. In the two most interesting cases of sextics in P4P4 and octics in P5P5, the bounds ...
    • Smooth models of singular K3-surfaces 

      Degtyarev, Alexander (European Mathematical Society Publishing House, 2019)
      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. ...
    • Tritangents to smooth sextic curves 

      Degtyarev, Alex (Association des Annales de l'Institut Fourier, 2022-10-21)
      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.