Talk:Ample vector bundle

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So, is this article talking about line bundles or vector bundles? --Ardonik 06:26, Aug 1, 2004 (UTC)

It's funny - nowhere in the article the notion of "ample vector bundle" is defined. I think it should be renamed to "ample line bundle", to avoid confusion. --Tiphareth 20:29, 18 April 2006 (UTC)

Well, there's a whole book about ample vector bundles by Hartshorne, so the more general concept exists. I don't have easy access to it; but more of an improvement to the article would be to add something, even if it is brief. Charles Matthews 19:02, 28 April 2006 (UTC)

There are several notions of ampleness in fact. The one due to Hartshorne is the following: a bundle is ample if the relative O(1) line bundle on its projectivization is ample.

This notion is much more exotic than the usual ampleness for line bundles, which is pretty much the most common and important notion in algebraic geometry. I believe the ample vector bundles should be defined in a separate article. --Tiphareth 04:11, 27 May 2006 (UTC)