Rank two vector bundles on \({\mathbb P}^ n\) uniform with respect to some rational curves. (English) Zbl 0637.14011
A classical method for studying the classifying vector bundles on projective spaces is to study their restrictions to linear subvarieties. For example, it is well known that a vector bundle on \({\mathbb{P}}^ n \) of rank \(r\leq n,\) whose restriction to all lines has the same splitting type is homogeneous.
Let E be a rank two vector bundle on \({\mathbb{P}}^ n,\) whose restriction to all rational smooth curves of degree \(d\) in \({\mathbb{P}}^ n \)has constant splitting type. In this paper we prove that if \(d=2\), or \(d=3\) and \(c_ 1(E)\) is even, then E is homogeneous.
Let E be a rank two vector bundle on \({\mathbb{P}}^ n,\) whose restriction to all rational smooth curves of degree \(d\) in \({\mathbb{P}}^ n \)has constant splitting type. In this paper we prove that if \(d=2\), or \(d=3\) and \(c_ 1(E)\) is even, then E is homogeneous.
Reviewer: M.Idà
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
References:
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