Browsing by Subject "Mukai group"

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    Conics on Barth-Bauer octics
    (Zhongguo Kexue Zazhishe / Science in China Press, 2024-04-23) Degtyarev, Alex
    We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by 176 and show that there is a unique surface with 176 conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane (ramified at a smooth sextic curve) that contains 8,910 smooth conics.
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    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.