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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