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arXiv · 2505.03487

Admissible covers and stable maps

Denis Nesterov·Maximilian Schimpf·Johannes Schmitt
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Abstract

Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on $\overline{M}_{g,n}$. 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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Denis Nesterov, Maximilian Schimpf, Johannes Schmitt. 2025-05-06. Admissible covers and stable maps. https://arxiv.org/abs/2505.03487

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