The pullback of a theta divisor to \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\overline{\mathcal {M}}_{g,n}}$\end{document}

We compute the class of a divisor on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\overline{\mathcal {M}}_{g,n}$\end{document} given as the closure of the locus of smooth pointed curves [ C ;  x 1 , …,  x n ] for which ∑ d j x j has an effective representative, where the d j 's are integers summing up to g − 1, not all positive. The techniques used are a vector bundle computation, a pushdown argument reducing the number of marked points, and the method of test curves.