invertible sheaf

A sheaf 𝔏 of 𝒪X modules on a ringed space 𝒪X is called if there is another sheaf of 𝒪X-modules 𝔏 such that 𝔏𝔏𝒪X. A sheaf is invertiblePlanetmathPlanetmath if and only if it is locally free of rank 1, and its inverseMathworldPlanetmathPlanetmathPlanetmath is the sheaf 𝔏om(𝔏,𝒪X), by the map.

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

Title invertible sheaf
Canonical name InvertibleSheaf
Date of creation 2013-03-22 13:52:34
Last modified on 2013-03-22 13:52:34
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 8
Author Mathprof (13753)
Entry type Definition
Classification msc 14A99