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We define tautological Chow classes on the moduli space of curves with linearseries. In the case where the forgetful morphism to the moduli space of curveshas relative dimension zero, we describe the images of these classes in theChow group of Mgbar. As an application, we compute the (virtual) slopes ofseveral different classes of divisors on Mgbar.

Tautological classes on moduli spaces of curves with linear series and a push-forward formula when $\rho=0$