Abstract
The classification problem for cubic surfaces with 27 lines is concerned with describing a complete set of the projective equivalence classes of such surfaces. Despite a long history of work, the problem is still open. One approach is to use a coarser equivalence relation based on geometric invariants. The Eckardt point configuration is one such invariant. It can be used as a coarse-grain case distinction in the classification problem. We provide an explicit parametrization of the equations of cubic surfaces with a given Eckardt point configuration over any field. Our hope is that this will be a step towards the bigger goal of classifying all cubic surfaces with 27 lines.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: The Art of Combinatorics - A Volume in Honour of Aart Blokhuis”.
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Betten, A., Karaoglu, F. The Eckardt point configuration of cubic surfaces revisited. Des. Codes Cryptogr. 90, 2159–2180 (2022). https://doi.org/10.1007/s10623-021-00999-w
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DOI: https://doi.org/10.1007/s10623-021-00999-w