2018/09/05 by Abel Castorena, Castorena, Abel, H. Torres-López +1
Mathematics · #14C20 #14H10 #14H51 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14C20 #msc:14H10 #msc:14H51 #msc:14H60
paper · pdf · doi:10.48550/arxiv.1809.01333
10 pages. Remove Lemma 2.5 and Theorem 2.7 related with the not injectivity of the theta map
openalex publication_date 2018/09/05 · arxiv created 2018/09/17 · arxiv updated 2018/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let C be a smooth complex irreducible projective curve of genus g with general moduli, and let (L,H0(L)) be a generated complete linear series of type (d,r+1) over C. The syzygy bundle, denoted by ML, is the kernel of the evaluation map H0(L)⊗\mathcal OC→ L. In this work we have a double purpose. The first one is to give new examples of stable syzygy bundles admitting theta divisor over general curves. We prove that if ML is strictly semistable then ML admits reducible theta divisor. The second purpose is to study the cohomological semistability of ML, and in this direction we show that when L induces a birational map, the syzygy bundle ML is cohomologically semistable, and we obtain precise conditions for the cohomological semistability of ML where such conditions agree with the semistability conditions for ML.