#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, I guess what I suggest boils down to:
* ''fibration'' - a surjective equidimensional morphism, a "global in
codomain" property check by `is_fibration`;
* ''fiber'' - a preimage of a single point, a "local in codomain"
construction well-defined for any morphism, regardless of its relation to
fibrations in any category. http://mathworld.wolfram.com/Fiber.html is an
easy to find reference, although not as authoritative as
Danilov&Shafarevich ;-)
Maybe it is a bit unfortunate that they have the same root, kind of like
reduced/reducible, but calling it `preimage_component(domain_cone)` is not
clear enough since then it may mean full preimage of an orbit or its
closure, and something like `point_preimage_component(domain_cone)` is
incomprehensible. Limiting to surjective morphisms and excluding a
morphism from a blowup chart just because of vocabulary issues is a bit
unsatisfactory...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:23>
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