Koszul Divisors on Moduli Spaces of Curves

In this paper we describe a general method of constructing special effective divisors on various moduli spaces using the syzygies of the parametrized objects. The method can be applied to a wide range of moduli problems with the property that the coarse moduli space has canonical singularities hence pluricanonical forms extend over any desingularization of the moduli space. Here we treat the case of the moduli stacks Mg,n and we develop the intersection theory machinery necessary to understand the compactification and compute the class of these Koszul divisors.