#12892: Toric fibration morphisms
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.3
Component: algebraic geometry | Resolution:
Keywords: sd40.5 | Work issues: comments and rebasing
Report Upstream: N/A | Reviewers: Andrey Novoseltsev
Authors: Volker Braun | Merged in:
Dependencies: #12361, #13023 | Stopgaps:
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Comment (by novoselt):
Well, what exactly do you mean by "fibration"? Fiber bundle? Fibration in
the sense of `is_fibration` with all fibers having the same dimension?
That excludes even blowups. Anything surjective? That excludes e.g. chart
inclusion, or maps from charts of blowups into the original variety. I
think for any morphism it is reasonable to look at fibers over any point
of the codomain, it is just the inverse image. And whether we return
something special or raise an exception, we still have to do the work of
figuring out what's going on.
From the user point of view, I think it is a bit easier/more elegant to
handle "corner case" outputs than exceptions, `fiber_component` and
`fiber_dimension` have pretty clear meaning in general. I think
`fiber_generic` has it as well. The `fiber_graph` one is indeed quite
special and maybe it makes sense to restrict it to surjective or even
`is_fibration` case.
In the case of factoring through the image, the middle variety can be
difficult to work with and I am not even sure if the current support is
sufficient for any work as well. Then again for the inclusion there is a
question of what is covered and what is not, and the natural test seems to
be - are there points of this point or not, but if fiber methods don't
work, then there should be something separate. I think it will be more
complicated.
E.g. take a blowup of a plane and consider the map from one of the charts
to the plane. How will it factor??? I suspect clear factorization into
surjection and injection requires working with complete fans and that's
definitely way too restrictive.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:20>
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