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Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves.
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J. Bryan and R. Pandharipande, The local Gromov-Witten theory of curves
2008
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A. Chiodo, Stable twisted curves and their r r -spin structures
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A. Chiodo, Towards an enumerative geometry of the moduli space of twisted curves and rth roots
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E. Clader and F. Janda, Pixton’s double ramification cycle relations
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2013
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S. Grushevsky and D. Zakharov, The double ramification cycle and the theta divisor
2014
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A. Buryak, S. Shadrin, L. Spitz, and D. Zvonkine, Integrals of ψ \psi -classes over double ramification cycles
2015
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R. Pandharipande, A. Pixton, and D. Zvonkine,
2015
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