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Abstract
In this paper we describe the space spanned by the divisors of curves and points satisfying certain ramification conditions on ℳ¯ g,n , the moduli space of n-pointed stable curves of genus g. This generalizes work of Eisenbud, Harris, and Mumford for the cases n ≤ 1.
Acknowledgments
This paper is a revised version of parts of my doctoral dissertation (Logan, Citation1999). I would like to thank Mira Bernstein for teaching me how to work with moduli spaces, Sean Keel for his insights and suggestions, and Ravi Vakil for his comments on a draft of this paper. In addition, I would like to thank the referee for a helpful report that directed me to previous work on the same subject and led me to improve the exposition. This work was partially supported by a Sloan Dissertation Fellowship and a VIGRE grant from the NSF.