invertible sheaf

A sheaf $\\mathfrak{L}$ of $\\mathcal{O}_{X}$ modules on a ringed space $\\mathcal{O}_{X}$ is called if there is another sheaf of $\\mathcal{O}_{X}$ -modules $\\mathfrak{L}^{\\prime}$ such that $\\mathfrak{L}\\otimes\\mathfrak{L}^{\\prime}\\cong\\mathcal{O}_{X}$ . A sheaf is invertible if and only if it is locally free of rank 1, and its inverse is the sheaf $\\mathfrak{L}^{\\vee}\\cong\\mathcal{H}om(\\mathfrak{L},\\mathcal{O}_{X})$ , by the map.

The set of invertible sheaves form an abelian group under tensor multiplication, called the Picard group of $X$ .

单词	InvertibleSheaf
释义	invertible sheaf A sheaf $\\mathfrak{L}$ of $\\mathcal{O}_{X}$ modules on a ringed space $\\mathcal{O}_{X}$ is called if there is another sheaf of $\\mathcal{O}_{X}$ -modules $\\mathfrak{L}^{\\prime}$ such that $\\mathfrak{L}\\otimes\\mathfrak{L}^{\\prime}\\cong\\mathcal{O}_{X}$ . A sheaf is invertible if and only if it is locally free of rank 1, and its inverse is the sheaf $\\mathfrak{L}^{\\vee}\\cong\\mathcal{H}om(\\mathfrak{L},\\mathcal{O}_{X})$ , by the map. The set of invertible sheaves form an abelian group under tensor multiplication, called the Picard group of $X$ .
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