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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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##### References:
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