Abstract
We give more detail to our examples in [1] of K3 surfaces over \(\mathbb C\) which have an infinite automorphism group that preserves some elliptic pencil of the K3 surface.
Similar content being viewed by others
References
V. V. Nikulin, “Quotient groups of the automorphism groups of hyperbolic forms by the subgroups generated by 2-reflections. Algebraic-geometric applications,” J. Soviet Math. 22 (4), 1401–1475 (1983).
V. V. Nikulin, “Some examples of K3 surfaces with infinite automorphism group which preserves an elliptic pencil,” arXiv:2006.03942 (2020).
I. R. Shafarevich (ed.), “Algebraic surfaces,” Proc. Steklov Math. Inst. 75, 3–215 (1965).
I. I. Pjatetskiĭ-Šapiro and I. R. Šafarevič, “A Torelli theorem for algebraic surfaces of type K3,” Math. USSR Izv. 5 (3), 547–588 (1971).
V. V. Nikulin, “Integral symmetric bilinear forms and some of their geometric applications,” Math. USSR Izv. 14 (1), 103–167 (1980).
N. Bourbaki, Groupes et algèbres de Lie, Groupes de Coxeter et systèmes de Tits, Groupes engendrés par des reflexions, systèmes de racines (Hermann, Paris VI, 1968).
G. Mezzedimi, “K3 surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers,” ArXiv:1912.08583v2 (2019), pp. 29 pages.
È. B. Vinberg “On groups of unit elements of certain quadratic forms,” Math. USSR-Sb. 16 (1), 17–35 (1972).
Funding
This work was supported by the Russian Science Foundation under grant 19-11-00237.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nikulin, V.V. Some Examples of K3 Surfaces with Infinite Automorphism Group which Preserves an Elliptic Pencil. Math Notes 108, 542–549 (2020). https://doi.org/10.1134/S0001434620090266
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434620090266