Stabilité des fibrés Λ^pE_L et condition de Raynaud

2003/09/17 by O. Schneider, Olivier Schneider, Schneider, Olivier
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cancer Treatment and Pharmacology #FOS: Mathematics #Spinal Hematomas and Complications #math.AG

paper · pdf · doi:10.48550/arxiv.math/0309277

11 pages

arxiv created 2003/09/17 · openalex publication_date 2003/09/17 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth curve of genus g ≥ 2 on \C. Let L be a line bundle on C generated by its global sections and let E_L be the dual of the kernel of the evaluation map e_L. We are studying here the relation between the stability the fact that the bundle is verifying a condition (R) introduced by Raynaud : we prove that E_L is semi stable when C is general. We also prove that E_L is verifying (R) when °(L) ≥ 2g or when L is generic. Finally we prove that for each p in \2,..., rg(E_L)-2\, if °(L) ≥ 2g+2 then Λ^pE_L is not verifying (R).

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