#12892: Toric fibration morphisms
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.11
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, #14353 | Stopgaps:
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Comment (by novoselt):
How about this compromise between surjective/general morphisms support -
compute fibers only for dominant ones. For a toric morphism being dominant
implies:
* surjection between tori, thus
* surjection onto any torus orbit if it was hit at all, so
* fiber/preimage over any point of any orbit is the same, including the
case when it is empty.
So there is no confusion with returning something when distinguished
points have something over them and some others don't. In terms of #14353
factorization, this means supporting compositions of surjective and
birational factors, but throwing exceptions if the last injective factor
is not an identity map on tori/lattices.
In particular, a blowup chart will be supported with single point fiber
over the torus, single point fiber over one of the axis, empty fiber over
another axis, and an affine line fiber over the origin. Awesome example
for some intro classes ;-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:32>
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