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.