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Rank 2 spanned vector bundles on {P}^2 with a fixed restriction to a line or a prescribed order of stability


Abstract


Fix a line D\subset \mathbb {P}^2. In this note we study rank 2 spanned vector bundles with prescribed Chern classes and either with a prescribed order of stability or whose restriction to D has a prescribed splitting type, mainly when the splitting type is either rigid or the most extremal one, (c,0). We use the description of the Chern classes of all rank 2 spanned bundles due to Ph. Ellia.

DOI Code: 10.1285/i15900932v36n1p25

Keywords: spanned vector bundles; vector bundles on the plane; splitting type

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