Talk:Positive form

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Please check the signs, I tend to mix them up. Tiphareth 17:13, 11 April 2007 (UTC)

[edit] A down to earth interpretation

Is this statement true?

 Suppose that a divisor $D$ on $M$ generates a positive line bundle $L$.  Then if $a$ is any homology class of $M$ that can be represented by a embedded Riemannian surface (perhaps with singularities), then $Da$ is greater or equal to zero.

in case this question is true, is this the main point of positive line bundles? That is, that if it has a divisor representing it, then it will have positive intersection with any other class that is represented by a complex submfld.

ELSE:

 If L is represented by a divisor, then $<c_1(L),[N]> \geq 0$ where $N$ is a complex subvariety.  Hence, if we want to know if $L = [D]$ for some divisor $D$ the first thing to check is if $L$ is positive since every $[D]$ is so.

is this the point of positive line bundles? 14:49, 27 February 2008 (UTC)