Admissible covers and stable maps

2025/05/06 by Denis Nesterov, Nesterov, Denis, Maximilian Schimpf +3
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2505.03487

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

Moduli spaces of admissible covers and stable maps of target curves give rise to cycles on 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.

Citations

• Hilbert schemes of points and Fulton-MacPherson compactifications
• Tautological and non-tautological cycles on the moduli space of abelian varieties
• Unramified Gromov-Witten and Gopakumar-Vafa invariants
• Quasimap wall-crossing for GIT quotients
• Intersections of loci of admissible covers with tautological classes
• Classes of Weierstrass points on genus 2 curves
• Logarithmic Stable Maps
• Relative maps and tautological classes
• The equivariant Gromov-Witten theory of P¹
• Gromov-Witten theory, Hurwitz theory, and completed cycles
• Twisted bundles and admissible covers
• Toda equations for Hurwitz numbers
• Hodge integrals and Hurwitz numbers via virtual localization
• Stable maps and branch divisors
• Localization of virtual classes
• Enumeration of rational curves via torus actions

Related

• Double ramification cycles on the moduli spaces of admissible covers
• Twisted bundles and admissible covers
• Cyclic covers of Stable curves and their moduli spaces
• Non-tautological Hurwitz cycles
• GIT Constructions of Moduli Spaces of Stable Curves and Maps