Fibrés vectoriels de rang deux sur ¶² provenant d'un revêtement double

2008/06/20 by Jean Vallès, Vallès, Jean
Engineering · Mathematics · #14D20 #14J60 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.AG #msc:14D20 #msc:14J60

paper · pdf · doi:10.48550/arxiv.0806.3355

quinze pages

openalex publication_date 2008/06/20 · arxiv created 2008/10/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since Schwarzenberger and his celebrated paper called "Vector bundles on the projective plane" we know that any rank two vector bundle on ¶² is a direct image of a line bundle on a double covering of the plane. This theorem suggests to study the rank two vector bundles according to the branch curve of the covering which they come from. Thus, in the first part we prove that, given a double covering ramified over an irreducible curve C_2r with degree 2r, the jumping lines of fixed order (order depending on r and on the parity of the rank two vector bundle) of the direct images vector bundles are necessarely r-tangent to C_2r. In the second part we concentrate on the case r=2. Then we give a list of vector bundles for which the jumping lines are exactly the bitangent lines to the branch quartic.

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