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Canonical bundle
(Redirected from Canonical divisor)
In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n is the line bundle
which is the nth exterior power of the cotangent bundle Ω on V. That is, it is the bundle of holomorphic n-forms on V, if V is defined over the complex number field. This is the dualising object for Serre duality on V. It may equally be considered an invertible sheaf.
The canonical class is the divisor class of a Cartier divisor K on V giving rise to the canonical bundle — it is an equivalence class for linear equivalence on V, and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor 
with 
canonical. The anticanonical bundle is the corresponding inverse bundle 
.
Last updated: 10-10-2005 02:05:26
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details