The Chow Ring of the Hilbert Cube
Abstract
Given a smooth projective variety $X$ over an algebraically closed field $k$, we compute the Chow ring of the Hilbert scheme of three points on $X$, $\operatorname{Hilb}^3(X)$, as an algebra with generators and relations over the Chow ring of $X\times\operatorname{Sym}^2(X)$. If in addition the characteristic of $k$ is zero, we extend the computation to the quasi-projective case.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 January 2026
- Document type
- Preprint