We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.
Cite this article
Davide Cesare Veniani, Symmetries and equations of smooth quartic surfaces with many lines. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 233–256DOI 10.4171/RMI/1127