Eckardt points on a cubic threefold
Gloire Grace Bockondas, Basile Guy Richard Bossoto
TL;DR
This paper surveys Eckardt points on smooth complex cubic threefolds, focusing on methods to compute all such points and constructing examples of threefolds without Eckardt points but with triple lines.
Contribution
It provides a systematic approach to compute Eckardt points and constructs novel examples of cubic threefolds with specific geometric properties.
Findings
Developed a method to compute all Eckardt points on a cubic threefold.
Constructed cubic threefolds with triple lines but no Eckardt points.
Enhanced understanding of the geometric configurations of cubic threefolds.
Abstract
In this paper we survey Eckardt points on a smooth complex cubic threefold with an approach aimed at computing all Eckardt points of a cubic threefold. In addition, we construct cubic threefolds with no Eckardt points but containing triple lines.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometric and Algebraic Topology