Abstract
AbstractLet X be a complex projective K3 surface and let $$T_X$$
T
X
be its transcendental lattice; the characteristic polynomials of isometries of $$T_X$$
T
X
induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The aim of this note is to answer this question, as well as related ones, and give an alternative approach to some results of Kondō, Machida, Oguiso, Vorontsov, Xiao and Zhang; this leads to questions and results concerning orthogonal groups of lattices.
Publisher
Springer Science and Business Media LLC
Reference26 articles.
1. Apostol, T.M.: Resultants of cyclotomic polynomials. Proc. Amer. Math. Soc. 24(3), 457–462 (1970)
2. Bayer-Fluckiger, E.: Isometries of lattices and Hasse principles. J. Eur. Math. Soc. https://doi.org/10.4171/JEMS/1334
3. Bayer-Fluckiger, E.: Automorphisms of $$K3$$ surfaces, signatures, and isometries of lattices (2022). arXiv:2209.06698v3 (to appear in J. Eur. Math. Soc.)
4. Bayer-Fluckiger, E., Taelman, L.: Automorphisms of even unimodular lattices and equivariant Witt groups. J. Eur. Math. Soc. 22, 3467–3490 (2020)
5. Brandhorst, S.: The classification of purely non-symplectic automorphisms of high order on $$K3$$ surfaces. J. Algebra 533, 229–265 (2019)