Browsing by Subject "Elliptic pencil"

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    Lines in supersingular quartics
    (Nihon Sugakkai,Mathematical Society of Japan, 2021-10-19) Degtyarev, Alex
    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 is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.
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    Lines on K3-quartics via triangular sets
    (Springer, 2024-10-06) Degtyarev, Alex; Rams, Slawomir
    We prove the sharp upper bound of at most 52 lines on a complex K3-surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics.
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    Lines on smooth polarized K3-surfaces
    (Springer, 2019) Degtyarev, Alex
    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 are 42 and 36, respectively, as conjectured in an earlier paper.