| The moduli spaces H_{d,g} of covers of genus g and degree d of the projective line are known as Hurwitz spaces. We will discuss the Maroni stratification on such Hurwitz spaces. This stratification has a stratum that is a divisor only if d - 1 divides g and we will approximate the class of this divisor in the compactified Hurwitz space. We will also construct an analogue of the above dvivisors on the Hurwitz spaces H_{d,g} for all pairs (d,g) with d less or equal than g, with a few exceptions. This is joint work with Gerard van der Geer. |