2024/12/04 by Marco Fava, Fava, Marco, Nicola Pagani +3 · 1 citation
Mathematics · #14D22 #14H10 #14H40 #14K10 #14Txx #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.03532
openalex publication_date 2024/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study a new class of compactified Jacobians for nodal curves, that we call compactified Jacobians of vine type, or simply V-compactified Jacobians. This class is strictly larger than the class of classical compactified Jacobians, as constructed by Oda-Seshadri, Simpson, Caporaso and Esteves. We characterize V-compactified Jacobians as the compactified Jacobians that can arise as limits of Jacobians of smooth curves under a one-parameter smoothing of the nodal curve, extending previous works on fine compactified Jacobians by Pagani-Tommasi and Viviani to the case of all compactified Jacobians.