[sage-support] Re: User question about toric varieties

[Andrey Novoseltsev]

This is a lng standing bug that nobody cared about enough to fix:
https://trac.sagemath.org/ticket/11394

On Friday, 1 July 2016 09:34:02 UTC-6, kcrisman wrote:
>
> On the sagenb github site (https://github.com/sagemath/sagenb/issues/402):
>
>
> Hi there,
>
> I tried to verify with Sage that P^2 is projective. Unfortunately, Sage 
> replied with 'false'. Here is what I tried:
>
> P2=toric_varieties.P2();
> P2.is_projective()
>
> The last line returned 'false'. The same happens for e.g. P1xP1.
>
> [I am running SageMath version 7.2, Release Date: 2016-05-15]
>
> Is this a bug? Thank you!
>

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[sage-support] Re: User question about toric varieties

[kcrisman]

Hi there,

> I tried to verify with Sage that P^2 is projective. Unfortunately, Sage 
> replied with 'false'. Here is what I tried:
>
> P2=toric_varieties.P2();
> P2.is_projective()
>
> The last line returned 'false'. The same happens for e.g. P1xP1.
>


This seems to be about an ambient space, and apparently only returns True 
if you are in a certain subclass of schemes, regardless.

sage: A.ambient_space()
2-d CPR-Fano toric variety covered by 3 affine patches

sage: A.is_projective??

Signature: A.is_projective()

Source:

def is_projective(self):

"""

Return whether this ambient space is projective n-space.


EXAMPLES::


sage: AffineSpace(3,QQ).is_projective()

False

sage: ProjectiveSpace(3,QQ).is_projective()

True

"""

# overloaded in the projective space derived class

return False
 

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