The Stack of Rational Curves

Abstract

In this series of three article, we start to investigate the rational Chow ring of the stack 𝔐₀ consisting of nodal curves of genus 0. In particular, we determine completely the rational Chow ring of the substack consisting of curves with at most 3 nodes. In the first article, we construct the stack 𝔐₀ and its stratification by nodes, and show that the map from the universal curve to the stack is not representable in the category of schemes.

ACKNOWLEDGMENTS

I am grateful to my thesis advisor, Angelo Vistoli, for his patient and constant guidance, and Rahul Pandharipande, who suggested the problem to him.

I also wish to thank Dan Edidin for very helpful remarks.

Notes

Communicated by S. L. Kleiman.