A universal formula for counting cubic surfaces
Abstract
Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family.As sample applications, we show that the PGL 4 orbit closure of a generic cubic surface has degree 96120, and that a general cubic surface arises 42120 times as a hyperplane section of a general cubic threefold.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Polynomial and algebraic computation
Publication details
- Journal / source
- Algebraic geometry
- Publisher
- Foundation Compositio Mathematica
- Pages
- 411–450
- Publication date
- 21 April 2026
- Language
- EN