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In algebraic geometry, a reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The second dual of a coherent sheaf is called the reflexive hull of the sheaf. A basic example of a reflexive sheaf is a locally free sheaf and, in practice, a reflexive sheaf is thought of as a kind of a vector bundle modulo some singularity. The notion is important both in scheme theory and complex algebraic geometry. A reflexive sheaf is torsion-free. The dual of a coherent sheaf is reflexive. Usually, the product of reflexive sheaves is defined as the reflexive hull of their tensor products (so the result is reflexive.) A coherent sheaf ''F'' is said to be "normal" in the sense of Barth if the restriction is bijective for every open subset ''U'' and a closed subset ''Y'' of ''U'' of codimension at least 2. With this terminology, a coherent sheaf on an integral normal scheme is reflexive if and only if it is torsion-free and normal in the sense of Barth. A reflexive sheaf of rank one on an integral locally factorial scheme is invertible. A divisorial sheaf on a scheme ''X'' is a rank-one reflexive sheaf that is locally free at the generic points of the conductor ''D''''X'' of ''X''. == See also == *Torsionless module *Torsion sheaf 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reflexive sheaf」の詳細全文を読む スポンサード リンク
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