Admissible covers and stable maps
Denis Nesterov, Maximilian Schimpf, Johannes Schmitt

TL;DR
This paper establishes a cycle-theoretic formula linking admissible covers and stable maps, unifying and refining existing formulas like the Gromov-Witten/Hurwitz correspondence, with computational verification in low-genus cases.
Contribution
It introduces a new cycle formula that generalizes and refines key existing results in the intersection theory of moduli spaces.
Findings
The formula recovers the Ekedahl-Lando-Shapiro-Vainshtein formula.
It provides a cycle-theoretic refinement of the Gromov-Witten/Hurwitz correspondence.
Computational checks confirm the formula in low-genus scenarios.
Abstract
Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on . 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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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology
