In mathematics, the Picard group of a ringed space X, written Pic(X), is the group formed by the isomorphism classes of invertible sheaves, also called line bundles, on X, with tensor product serving as the group operation. It is a global analogue of constructions such as the divisor class group and the ideal class group, and it plays a central role in algebraic geometry and in the theory of complex manifolds, where it helps classify the line bundles that can exist on a given space.
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Object KindStructure or Algebraic Object 1 Connections
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Source Picard Group (Wikipedia)
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Source Picard Group (Wikipedia)
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1. Picard Group (Wikipedia)
Lead section
In mathematics, the Picard group of a ringed space X, denoted by Pic(X), is the group of isomorphism classes of invertible sheaves (or line bundles) on X, with the group operation being tensor product.
In Branch: Algebraic Geometry, Lead paragraph
This construction is a global version of the construction of the divisor class group, or ideal class group, and is much used in algebraic geometry and the theory of complex manifolds.
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