2003/09/14 by Tom Graber, Ravi Vakil, Graber, Tom +1 · 3 citations
Mathematics · #14D22 #14F43 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 14H10 #Secondary 14C15 #math.AG #msc:14C15 #msc:14D22 #msc:14F43 #msc:14H10
paper · pdf · doi:10.48550/arxiv.math/0309227
31 pages, 5 figures. Revision corrects several typos
openalex publication_date 2003/09/14 · arxiv created 2005/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves vanish away from strata corresponding to curves with at least i-g+1 genus 0 components. (The proof of this result is quite short and naive.) As consequences, we prove and generalize various conjectures and theorems about various moduli spaces of curves (due to Getzler, Ionel, Faber, Looijenga, Pandharipande, Diaz, and others). This theorem appears to be the geometric content behind these results; the rest is straightforward graph combinatorics. The theorem also suggests the importance of the stratification of the moduli space by number of rational components.