1997/09/08 by Eduardo Esteves, Esteves, Eduardo · 2 citations
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9709009
AMS-TeX, 41 pages - address: [email protected]
arxiv created 1997/09/08 · openalex publication_date 1997/09/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct natural relative compactifications for the relative Jacobian over a family X/S of reduced curves. In contrast with all the available compactifications so far, ours admit a universal sheaf, after an etale base change. Our method consists of considering the functor F of relatively simple, torsion-free, rank 1 sheaves on X/S, and showing that certain open subsheaves of F have good properties. Strictly speaking, the functor F is only representable by an algebraic space, but we show that F is representable by a scheme after an etale base change. Finally, we use theta functions originating from vector bundles to compare our new compactifications with the available ones.