2004/10/25 by Eduardo Esteves, Steven L. Kleiman, Esteves, Eduardo +2 · 1 citation
Mathematics · #14H20 (Secondary) #14H40 (Primary) 14K30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14H20 #msc:14H40 #msc:14K30
paper · pdf · doi:10.48550/arxiv.math/0410537
Plain TeX, 16 pages
arxiv created 2004/10/25 · openalex publication_date 2004/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the associated Abel map AL : C -> P, which maps C into its compactified Jacobian scheme P, and form its pullback map AL^* : Pic0P -> J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, double points, then AL^* is known to be an isomorphism. We prove that AL^* always extends to a map between the natural compactifications, Pic-P -> P, and that the extended map is an isomorphism if C has, at worst, ordinary nodes and cusps.