Re: complex projective geometry question


On Tue, 15 Mar 2005, Stephen Blake wrote:

> Andrew Scott <ascott@xxxxxxxxxxxxxxxxxxx> wrote in message news:<Pine.LNX.4.44.0503132311020.16112-100000@xxxxxxxxxxxxxxxxxxx>...
>> Alternatively, we want 2n points in CP^{n-1} so that almost all other
>> points in CP^{n-1} are uniquely determined by their projective distances
>> with respect to the 2n points.
>
> In my understanding, only n reference points are needed to fix a general
> point in CP^{n-1}, but I don't know what you mean by projective distance, so
> perhaps that is what I'm missing.

By "projective distance" in CP^{n-1} I mean just a distance specified by
the acute angle between the corresponding lines in C^n. Specifically, if x
and y are unit vectors in C^n, I'm taking the distance between the
corresponding lines to be 1-|(x,y)|.

So we will need at least 2n-2 lines to specify another through the acute
angles simply by counting the parameters. However I think we need at least
2n-1 (though I'm allowing 2n). References for any of the cases of 2n-1,
2n, 2n+1, ... lines will be helpful.

thanks
andrew.

.