1997/09/05 by Eduardo Esteves, Esteves, Eduardo
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9709005
AMS-TeX, 11 pages - address: [email protected]
arxiv created 1997/09/05 · openalex publication_date 1997/09/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Jacobian J of a complete, smooth, connected curve X admits a canonical divisor Θ, called the Theta divisor. It is well-known that Θ is ample and, in fact, 3Θ is very ample. For a general complete, integral curve X, D'Souza constructed a compactification J of the Jacobian J by considering torsion-free, rank 1 sheaves on X. Soucaris and the author considered independently the analogous Theta divisor Θ on J, and showed that Θ is ample. In this article, we show that nΘ is very ample for n greater or equal to a specified lower bound. If X has at most ordinary nodes or cusps as singularities, then our lower bound is 3. Our main tool is to use theta sections associated to vector bundles on X to embed J into a projective space.