The Eckardt point configuration of cubic surfaces revisited

被引：0
作者：
Anton Betten
Fatma Karaoglu
机构：
[1] Kuwait University,Department of Mathematics
[2] Namik Kemal University,Department of Mathematics
[3] Colorado State University,Department of Mathematics
来源：
Designs, Codes and Cryptography | 2022年 / 90卷
关键词：
Finite geometry; Cubic surface; Eckardt point; Classification; Normal form; 05B25; 05E18; 14E05; 14J26; 51E25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：2159 / 2180
页数：21
相关论文
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