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Tautological and non-tautological cohomology of the moduli space of curves

By C. Faber and R. Pandharipande

Abstract

After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first is via curve counting over finite fields. The second is by obtaining length bounds on the action of the symmetric group S_n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found.Comment: 40 page

Topics: Mathematics - Algebraic Geometry
Year: 2011
OAI identifier: oai:arXiv.org:1101.5489

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