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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.

MSC:
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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