Revista Matemática Iberoamericana
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Published online: 2019-09-20
Symmetries and equations of smooth quartic surfaces with many linesDavide Cesare Veniani (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