Constructions of nontautological classes on moduli spaces of curves

Abstract

We construct explicit examples of algebraic cycles in \bar M_g (for large g congruent to 2 mod 4) and in M_2,20 (no bar) which are not in the tautological ring. In an appendix we give a general method for computing intersections in the tautological ring.

This supersedes our earlier preprint, "A non-tautological algebraic class on $\bar{M}_{2,22}$." This version gives more general constructions of nontautological classes on various moduli spaces of pointed curves