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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2023; 60(4): 695-743

Online first article June 21, 2023      Printed July 1, 2023

https://doi.org/10.4134/JKMS.j220014

Copyright © The Korean Mathematical Society.

Complex reflection groups and K3 surfaces II. The groups ${\boldsymbol{G_{29}}}$, ${\boldsymbol{G_{30}}}$ and ${\boldsymbol{G_{31}}}$

Cédric Bonnafé, Alessandra Sarti

IMAG, Universit'e de Montpellier; UMR 7348 CNRS, TSA 61125, 11 bd Marie et Pierre Curie

Abstract

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We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W.~Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.

Keywords: K3 surfaces, reflection groups, elliptic fibrations

MSC numbers: Primary 14J28; Secondary 20F55

Supported by: The first author is partly supported by the ANR: project No. ANR-16-CE40-0010-01 (GeRepMod) and ANR-18-CE40-0024-02 (CATORE). The second author is partly supported by the ANR: project No. ANR-20-CE40-0026-01 (SMAGP).

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