The Integral Chow Ring of the Stack of at Most 1-Nodal Rational Curves

Abstract

We give a presentation for the stack of rational curves with at most 1 node as the quotient by GL₃ of an open set in a 6-dimensional irreducible representation. We then use equivariant intersection theory to calculate the integral Chow ring of this stack.

Key Words:

• Algebraic stacks
• Chow rings

2000 Mathematics Subject Classification:

• Primary 14C15, 14A20
• Secondary 55N91

Notes

¹That is to say of arithmetic genus 0.

²This means that every GL _n -torsor is locally trivial in the Zariski topology.

Communicated by S. Kleiman.