Talk:Tautological line bundle

In complex geometry (see for example the book "Complex Geometry" by Huybrechts) the canonical line bundle of a complex manifold $X$ with complex dimension $n$ is just $\Wedge^n T^{(1,0) \ *}X$ (i.e. the top exterior power of the dual of the holomorphic tangent space). Notice that this is a complex line bundle, hence each fiber is a 2-dimensional real space.

In complex geometry, a tautological line bundle over a complex projective space is the dual of what is being called the canonical line bundle here. At least this is the definition found in Huybrechts' book. Perhaps a warning note should be placed in this article. —The preceding unsigned comment was added by 155.198.157.113 (talk • contribs) 19:48, 19 July 2006 (UTC)

That concept is described at canonical bundle. -- Fropuff 06:54, 14 February 2007 (UTC)

Name change proposal

I propose we move this article to tautological line bundle and then either redirect canonical line bundle to canonical line bundle or make it into a disambig page. I would prefer the former. We can put a disambig notice at the top of the canonical bundle article. -- Fropuff 06:54, 14 February 2007 (UTC)

I agree. Geometry guy 00:47, 14 May 2007 (UTC)

Yes, definitely. Also the term canonical line bundle is ambiguous even within algebraic geometry. There's the Canonical sheaf to deal with (which, it just so happens, is also a line bundle). I think tautological is a better term for what the present article deals with, since it really isn't canonical at all: it depends on the structure of projective space. Silly rabbit 19:04, 25 May 2007 (UTC)

Correct definition

The definition of the tautological bundle is missing the subset $\lbrace (x,0):x\in \mathbb {CP} ^{n}\rbrace$ since the vector $0$ don't belong to any class. NeoBeowulf (talk) 14:57, 29 September 2014 (UTC)