Rank   spanned vector bundles on   with a fixed restriction to a line or a prescribed order of stability

doi:10.1285/i15900932v36n1p25

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

Edoardo Ballico

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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Note di Matematica

Rank spanned vector bundles on with a fixed restriction to a line or a prescribed order of stability

Abstract

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