2004/12/14 by L. Brambila‐Paz, Brambila-Paz, L.
Mathematics · #14H60 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.math/0412285
openalex publication_date 2004/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a general smooth projective algebraic curve of genus g>1. We prove that the moduli space G(α:n,d,k) of α-stable coherent systems of type (n,d,k) over X is empty if k>n and the Brill-Noether number is negative. Moreover, if the Brill-Noether number is positive and 0, G(α:n,d,k) is non-empty G(α:n,d,k) is non-empty for all α>0 and G(α:n,d,k)= G(α':n,d,k) for all α,α'>0 and the generic element is generated.