 On the boundary of the moduli space, where curves may degenerate to reducible curves, there is a substack parametrizing reducible curves with a genus formula_125 component and a genus formula_126 component intersecting at one point, and the map sends the genus formula_126 curve to a point.Since all such genus formula_126 curves are parametrized by formula_129, and there is an additional formula_126 dimensional choice of where these curves intersect on the genus formula_126 curve, the boundary component has dimension formula_132.Constructing weighted projective spaces involves taking the quotient variety of some formula_133 by a formula_98-action.