On the deformation of orthogonal bundles over the projective line.
On the deformation of orthogonal bundles over the projective line.
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关于投影线上正交束的变形。
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
K. Hulek
中科院分区：
文献类型：
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作者：
K. Hulek
In a problem list which originated from the Oxford Conference on vector bundles in 1978 Barth (cf. [6], problem 20) proposed to study the deformation of orthogonal vector bundles over P1 = P1(C). The reason was the following: In [2] Barth and Elencwajg proved that a family of stable rank 2 vector bundles over P3 with first Chern class 0 and second Chern class n leads in a natural way to a family of orthogonal rank n bundles over P1. It follows from a well-known result of Mumford [8], p. 184 that if E is an orthogonal bündle then h°(E(— 1)) mod 2 is invariant under deformations. By the construction of Barth-Elencwajg this implies that for a stable rank 2 bündle over P3 with c1(/) = 0 the value of h (F( — 2)) mod 2 is invariant under deformations. This, in fact, is a topological invariant and has long since been known äs the so-called Atiyah-Rees invariant [1].
