Weighted pointed stable curve invariants satisfy generalized Virasoro constraints and the KdV hierarchy, reducing to the unweighted Witten-Kontsevich theory after an explicit change of variables.
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Virasoro constraints for moduli of weighted pointed stable curves
Weighted pointed stable curve invariants satisfy generalized Virasoro constraints and the KdV hierarchy, reducing to the unweighted Witten-Kontsevich theory after an explicit change of variables.