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Special cases of the orbifold version of Zvonkine’s \(r\)-ELSV formula. (English) Zbl 1483.14092

Summary: We prove the orbifold version of Zvonkine’s \(r\)-ELSV formula in two special cases: the case of \(r=2\) (completed 3-cycles) for any genus \(g\geq 0\) and the case of any \(r\geq 1\) for genus \(g=0\).

MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
05E05 Symmetric functions and generalizations
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
30F30 Differentials on Riemann surfaces
14H70 Relationships between algebraic curves and integrable systems
14J33 Mirror symmetry (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
81T45 Topological field theories in quantum mechanics
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References:

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