Twenty-Seven Questions about the Cubic Surface

Abstract

We present a collection of research questions on cubic surfaces in 3-space. These questions inspired a collection of papers to be published in a special issue of the journal Le Matematiche. This article serves as the introduction to that issue. The number of questions is meant to match the number of lines on a cubic surface. We end with a list of problems that are open.

arXiv comment13 pages

References in corpus (11)

• Real Algebraic Surfaces
• Luigi Cremona and cubic surfaces
• Anticanonical tropical cubic del Pezzos contain exactly 27 lines
• Prym varieties of genus four curves
• Ranks and Singularities of Cubic Surfaces
• On realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form
• Computing invariants of cubic surfaces
• Determinantal representations of the cubic discriminant
• 96120: The degree of the linear orbit of a cubic surface
• Towards classifying toric degenerations of cubic surfaces
• The Newton polytope of the discriminant of a quaternary cubic form

Cited by in corpus (1)

• On realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form