Moduli of genus one curves with two marked points as a weighted blow-up

Abstract

We give an explicit description of ${\overline{\mathcal{M}}}_{1,2}$ as a weighted blow-up of a weighted projective stack. We use this description to compute the Brauer group of ${\overline{\mathcal{M}}}_{1,2;S}$ over any base scheme $S$ where 6 is invertible, and the integral Chow rings of ${\overline{\mathcal{M}}}_{1,2}$ and ${\mathcal{M}}_{1,2}$.

arXiv commentExpository changes, final version to appear in Mathematische Zeitschrift. Comments are welcome!