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

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

2011-01-28

arxiv.org/abs/1101.5489v1

Mathematics

Algebraic Geometry

40 pages

Scientific paper

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.

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