島根大学文理学部紀要. 理学科編

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島根大学文理学部紀要. 理学科編 10
1976-12-20 発行

ある種の楕円曲面上の複素平面束について

On Plane Bundles over Some Elliptic Surfaces
松永 弘道
ファイル
内容記述(抄録等)
M. F. Atiyah has given the cuassification theorem for holomorphic vector bundles over an elliptic curve, (Theorem 7, [2]). In the proof, two lemmas are effective, which are called the uniqueness and existence theorems. These are the motive for this paper. In §1, we prove that, over a product surface of a non singular curve and an elliptic curve, if a line bundle satisfies some condltion about a local triviality and the Chern class, then it admits a non trivial extension to a-plane bundle. This fact corresponds to Lemma 16, [2] . In §2, we define a strongly reducible plane bundle and prove that not every plane bundle is strongly reducible over a basic member (8, [4]) on an algebraic curve of genus greater than one. This fact corresponds to Lemma 15, [2].