The Eckardt Point Configuration of Cubic Surfaces Revisited

Dr. Fatma Karaoğlu

18 February 2022 16:00

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 coarserequivalence 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. This is a joint work with Anton Betten from Kuwait University.