Scheme.is_projective() should use mathematical definition

[novoselt]

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.

CC: @mminzlaff

Component: algebraic geometry

Stopgaps: todo

Issue created by migration from https://trac.sagemath.org/ticket/11394

[sagetrac-jakobkroeker]

Stopgaps: todo