Opened 9 years ago

Last modified 4 years ago

#11394 new defect

Scheme.is_projective() should use mathematical definition

Reported by: novoselt Owned by: AlexGhitza
Priority: major Milestone: sage-6.4
Component: algebraic geometry Keywords:
Cc: minz Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps: todo

Description

The current implementation of is_projective in

sage.schemes.generic.algebraic_scheme.AlgebraicScheme

is

return self.ambient_space().is_projective()

which in turn works as

    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

Both are wrong. It is possible to have a projective scheme sitting in a non-projective variety, as well as an ambient space which is projective, yet it is not a projective n-space.

There are methods that rely on this behavior, so they should be fixed and the above methods changed so that they either answer the question "Is X a projective scheme?" in the mathematical sense or raise a NotImplementedError if the answer is unknown.

Change History (6)

comment:1 Changed 8 years ago by minz

  • Cc minz added

comment:2 Changed 6 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:3 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:4 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:5 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:6 Changed 4 years ago by jakobkroeker

  • Stopgaps set to todo
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