2022/08/20 by Vance Blankers, Blankers, Vance, Sebastian Bozlee +1
Mathematics · #14H10 (primary) #14T90 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2208.09745
openalex publication_date 2022/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study all ways of constructing modular compactifications of the moduli space Mg,n of n-pointed smooth algebraic curves of genus g by allowing markings to collide. We find that for any such compactification, collisions of markings are controlled by a simplicial complex which we call the collision complex. Conversely, we identify modular compactifications of Mg,n with essentially arbitrary collision complexes, including complexes not associated to any space of weighted pointed stable curves. These moduli spaces classify the modular compactifications of Mg,n by nodal curves with smooth markings as well as the modular compactifications of M1,n with Gorenstein curves and smooth markings. These compactifications generalize previous constructions given by Hassett, Smyth, and Bozlee--Kuo--Neff.