A CALCULUS FOR THE MODULI SPACE OF CURVES

The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli space Mg and its compactification Mg, defining what seem to be the most important classes in this ring and calculating the class of some geometrically important loci in Mg in terms of these classes. We take as a model for this the enumerative geometry of the Grassmannians. [65]

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