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Constructions of nontautological classes on moduli spaces of curves. (English) Zbl 1079.14511
Summary: We construct explicit examples of algebraic cycles in \(\overline{M}_g\) (for large \(g\equiv 2 \pmod 4\)) and in \(M_{2,20}\) which are not in the tautological ring. In an appendix we give a general method for computing intersections in the tautological ring.

14H10 Families, moduli of curves (algebraic)
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14C15 (Equivariant) Chow groups and rings; motives
14C25 Algebraic cycles
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