- #1

Ssnow

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Thank you in advance.

Ssnow

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- #1

Ssnow

Gold Member

- 532

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Thank you in advance.

Ssnow

- #2

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So I'd need a lot of clarification before understanding your post.

- #3

Ssnow

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- #4

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Sorry, Ssnow, I am just as confused as before.

- #5

Ssnow

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- #7

Ssnow

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points ##[p_{0}:p_{1}]## only with ##p_{0}>0,p_{1}>0##Do you mean to take only those points in Pn\mathbb{P}^n with nonzero homogeneous coordinates (with respect to some base)? I don't understand why you say positive, since positivity is not a projective concept.

- #8

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So that would be a subset of the affine space, namely ##[p_0/p_1: 1] = [a:1]## with ##a>0##. So in this case, we will obtain ##\mathbb{R}^+##.points ##[p_{0}:p_{1}]## only with ##p_{0}>0,p_{1}>0##

- #9

Ssnow

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ok ##\mathbb{R}^{+}## is not so interesting but I was thinking what happen to a curve in ##\mathbb{P}^{1}## when you restrict the attention only to this subset, I cannot visualizing if a part of it collapse or nothing happens ... ,

- #10

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What do you mean with a curve? Any smooth curve? Or an algebraic curve determined by a polynomial?

ok ##\mathbb{R}^{+}## is not so interesting but I was thinking what happen to a curve in ##\mathbb{P}^{1}## when you restrict the attention only to this subset, I cannot visualizing if a part of it collapse or nothing happens ... ,

You know ##\mathbb{P}^1## is a circle, so there are curves which do not collapse to a point. On the other hand, ##\mathbb{R}^+## is contractible. Any curve can collapse to a constant curve.

- #11

Ssnow

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Thanks

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