Revista Matemática Iberoamericana


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Volume 36, Issue 1, 2020, pp. 233–256
DOI: 10.4171/rmi/1127

Published online: 2019-09-20

Symmetries and equations of smooth quartic surfaces with many lines

Davide Cesare Veniani[1]

(1) Johannes Gutenberg-Universität Mainz, Germany

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.

Keywords: Quartic surface, line, equation, K3 surface, automorphism

Veniani Davide Cesare: Symmetries and equations of smooth quartic surfaces with many lines. Rev. Mat. Iberoam. 36 (2020), 233-256. doi: 10.4171/rmi/1127