Аннотация:
This paper consists mainly of a review and applications of our old results relating to the title. We discuss how many elliptic fibrations and elliptic fibrations with infinite automorphism groups (or Mordell–Weil groups) an algebraic K3 surface over an algebraically closed field can have. As examples of applications of the same ideas, we also consider K3 surfaces with exotic structures: with a finite number of non-singular rational curves, with a finite number of Enriques involutions, and with naturally arithmetic automorphism groups.
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Тип публикации:
Статья
Язык публикации: английский
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pems4
Эта публикация цитируется в следующих 11 статьяx:
Adrian Clingher, Andreas Malmendier, “On Néron–Severi lattices of Jacobian elliptic K3 surfaces”, manuscripta math., 173:3-4 (2024), 847
Xun Yu, “K3 surface entropy and automorphism groups”, J. Algebraic Geom., 2024
Xi Chen, Frank Gounelas, Christian Liedtke, “Curves on K3 surfaces”, Duke Math. J., 171:16 (2022)
Xavier Roulleau, “On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations”, Int. J. Math., 33:06 (2022)
Giacomo Mezzedimi, “K3 Surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers”, Journal of Algebra, 587 (2021), 344
Martin Bright, Adam Logan, Ronald van Luijk, “Finiteness results for K3 surfaces over arbitrary fields”, European Journal of Mathematics, 6:2 (2020), 336
Xun YU, “Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree”, J. Math. Soc. Japan, 70:3 (2018)
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