Are there interesting cycles (other then the famous ones such as: Harris and Mumford's gonality divisor, the Gieseker-Petri divisor [which can be realized as the branch locus of a forgetful map from the space of admissible covers], and the Hain-Pixton double ramification locus) in $A^*(\overline{M}_{g,n})$ coming from Hurwitz theory?
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1$\begingroup$ Kazarian has used the ELSV formula to prove results about the Chow rings of Deligne-Mumford moduli spaces. Is that what you are asking about? $\endgroup$– Jason StarrCommented Mar 4, 2017 at 12:38
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1$\begingroup$ The double ramification cycle in $A^g(\overline M_{g,n})$ is certainly an interesting (tautological) cycle, which in some sense "comes" from Hurwitz theory. $\endgroup$– Andrea RicolfiCommented Mar 4, 2017 at 13:01
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$\begingroup$ Hi Jason, not exactly (I was thinking more of things like divisors in $\overline{M}_g$ that come from Hurwitz theory), but that sounds interesting. I'll take a look, thanks! $\endgroup$– NatiCommented Mar 5, 2017 at 4:41
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$\begingroup$ Hi Andrea, yes the double ramification cycle is one such example ... it's actually the only one I heard of :-) I was wondering if there are others (maybe more classical?) $\endgroup$– NatiCommented Mar 5, 2017 at 4:43
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