# On the cohomology rings of Grassmann varieties and Hilbert schemes

## TL;DR

This paper uses vector field techniques to compute the cohomology rings of Hilbert schemes of points in the projective plane, relating them to Grassmann varieties.

## Contribution

It introduces a novel approach connecting cohomology rings of Hilbert schemes with Grassmann varieties via vector field methods.

## Key findings

- Computed the ordinary cohomology rings of Hilbert schemes.
- Established relations between Hilbert schemes and Grassmann varieties.
- Provided explicit descriptions of equivariant cohomology rings.

## Abstract

By using vector field techniques, we compute the ordinary and equivariant cohomology rings of Hilbert scheme of points in the projective plane in relation with that of a Grassmann variety.