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Designs, Codes and Cryptography

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05-01-2022

The Eckardt point configuration of cubic surfaces revisited

Authors: Anton Betten, Fatma Karaoglu

Published in: Designs, Codes and Cryptography | Issue 9/2022

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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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Title: The Eckardt point configuration of cubic surfaces revisited
Authors: Anton Betten
Fatma Karaoglu
Publication date: 05-01-2022
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 9/2022
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-021-00999-w

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