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 \({\mathcal {M}}_{1,2}\).