Browsing by Subject "Conic"
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Item Open Access 800 conics on a smooth quartic surface(Elsevier BV * North-Holland, 2022-03-10) Degtyarev, AlexWe construct an example of a smooth spatial quartic surface that contains 800 irreducible conics. © 2022 Elsevier B.V.Item Open Access Conics on Barth-Bauer octics(Zhongguo Kexue Zazhishe / Science in China Press, 2024-04-23) Degtyarev, AlexWe 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.Item Embargo Conics on Kummer quartics(Tohoku Daigaku Suugaku Kyoshitsu,Tohoku University, Mathematical Institute, 2023-09-25) Degtyarev, AlexWe classify the configurations of lines and conics in smooth Kummer quartics, assuming that all 16 Kummer divisors map to conics. We show that the number of conics on such a quartic is at most 800.