Admissible covers and stable maps
Abstract
Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on Mg,n. We prove a formula relating these cycles. It recovers both the Ekedahl-Lando-Shapiro-Vainshtein formula and the Gromov-Witten/Hurwitz correspondence, providing a cycle-theoretic refinement thereof. The formula is verified computationally in low-genus cases with the help of Johannes Schmitt.
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