The Chow Ring of the Hilbert Scheme of Rational Normal Curves

TL;DR

This paper computes the integral Chow ring of the Hilbert scheme of rational normal curves in projective space using equivariant Chow ring techniques, and also provides algebraic computations for certain algebraic groups.

Contribution

It introduces a new presentation of the Chow ring of the Hilbert scheme of rational normal curves using equivariant methods and computes related algebraic group Chow rings.

Findings

Presented the integral Chow ring of H(d) for rational normal curves.

Computed equivariant Chow rings of O(n) and SO(2k+1).

Applied results to PGL(2) for Hilbert scheme analysis.

Abstract

Let H(d) be the (open) Hilbert scheme of rational normal curves of degree d in P^d. A presentation of the integral Chow ring of H(d) is given via equivariant Chow ring computations. Included also in the paper are algebraic computations of the integral equivariant Chow rings of the algebraic groups O(n), SO(2k+1). The results for S0(3)=PGL(2) are needed for the Hilbert scheme calculation.