# The Chow Ring of the Hilbert Scheme of Rational Normal Curves

@article{Pandharipande1996TheCR, title={The Chow Ring of the Hilbert Scheme of Rational Normal Curves}, author={Rahul Pandharipande}, journal={arXiv: Algebraic Geometry}, year={1996} }

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.

## 8 Citations

The Integral Chow Ring of the Stack of 1-Pointed Hyperelliptic Curves

- Mathematics
- 2020

In this paper we give a complete description of the integral Chow ring of the stack $\mathscr{H}_{g,1}$ of 1-pointed hyperelliptic curves, lifting relations and generators from the Chow ring of…

On the Chow ring of the classifying stack of PGL_3

- Mathematics
- 1999

We compute generators for the Chow ring of the classifying space of PGL_3 (over the complex numbers) as defined by Totaro. We also find enough relations after inverting 3. We show that this ring is…

The enumerative geometry of rational and elliptic curves in projective space

- Mathematics
- 1997

We study the geometry of varieties parametrizing degree d rational and elliptic curves in P^n intersecting fixed general linear spaces and tangent to a fixed hyperplane H with fixed multiplicities…

The Equivariant Chow Ring of So(4) Rahul Pandharipande

- Mathematics
- 1996

Let G be a reductive algebraic group. The algebraic analogue of EG is attained by approximation. Let V be a C-vector space. Let G × V → V be an algebraic representation of G. Let W ⊂ V be a…

Equivariant intersection theory

- Mathematics
- 1996

In this paper we develop an equivariant intersection theory for actions of algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are…

The Equivariant Chow Ring of SO(4)

- Mathematics
- 1996

The integral equivariant Chow ring of S0(4) is computed via the geometry of ruled quadric surfaces in P^3.

Se p 19 96 Equivariant Intersection Theory

- Mathematics
- 1998

The purpose of this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow…

Problems in arithmetic topology

- Mathematics
- 2021

We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on “Arithmetic Topology.” Three problem sessions were hosted during the workshop in which participants…

## References

SHOWING 1-10 OF 12 REFERENCES

Equivariant intersection theory

- Mathematics
- 1996

In this paper we develop an equivariant intersection theory for actions of algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are…

The Chow Ring of the Non-Linear Grassmannian

- Mathematics
- 1996

Let M_{P^k}(P^r, d) be the moduli space of unparameterized maps \mu:P^k -> P^r satisfying \mu^*(O(1))= O(d). M_{P^k}(P^r,d) is a quasi-projective variety, and, in case k=1, M_{P^1}(P^r,d) is the…

Geometric Invariant Theory

- Mathematics
- 1965

“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to…

Enumerative geometry of degeneracy loci

- Mathematics
- 1988

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1988, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…

Characteristic classes of principal bundles in algebraic geometry, preprint

- Characteristic classes of principal bundles in algebraic geometry, preprint
- 1995

Ann. Scient. Ec. Norm. Sup

- Ann. Scient. Ec. Norm. Sup
- 1988

Characteristic classes of principal bundles in algebraic geometry

- preprint
- 1995

The Chow Ring of the Symmetric Group, preprint 1994

- The Chow Ring of the Symmetric Group, preprint 1994

The Chow Ring of the Symmetric Group

- preprint
- 1994

Proposition 4. Let G × X → X be an algebraic group action with geometric quotient X → Y . If the action is free, then X → Y is a (´ etale locally trivial) principal G-bundle

- Proposition 4. Let G × X → X be an algebraic group action with geometric quotient X → Y . If the action is free, then X → Y is a (´ etale locally trivial) principal G-bundle