1999/11/10 by E. Esteves, Eduardo Esteves, Mathieu Gagné +6
Computer Science · Mathematics · #14H40 (Primary) 14H20 (Secondary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H20 #msc:14H40
paper · pdf · doi:10.48550/arxiv.math/9911069
Plain TeX, 32 pages. This is the final version, to appear in the Hartshorne issue of the Communications in Algebra. A number of small improvements to the original exposition were made here and there. In addition, Lemma (3.7) was corrected by reformulating it over an algebraically closed base field, and its proof revised accordingly. Since (3.7) was used in the proofs of Proposition (6.2) and Theorem (6.3), those proofs were revised too, (6.2) extensively and (6.3) minimally
openalex publication_date 1999/11/10 · arxiv created 2000/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m,1) to the corresponding presentation scheme. Fourth we prove that, if a curve is blown up at a double point, then the corresponding presentation scheme is a IP1-bundle. Finally, using Abel maps of bidegree (m,1), we characterize the curves having double points at worst