#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 vbraun):
There isn't really a universally accepted definition of "fibration", it
depends on the category you are in. In algebraic topology it is a morphism
with the homotopy lifting property, but in algebraic geometry the
underlying topological space of a fibration usually is not a fibration in
the topology sense. As another data point,
[[http://books.google.com/books?id=ZhzXJHUgcRUC&lpg=PA137&ots=aWMqiSqste&dq=fibration%20of%20curves&pg=PA137#v=onepage&q=fibration%20of%20curves&f=false|Danilov&Shafarevich
define a fibration of curves]] to be onto.
Also, ''elliptic fibration'' definitely implies surjective to me. Or, in
other words, if you excise complete preimages in the codomain then this is
not what I would call an elliptic fibration. Though of course YMMV.
Regardless of the category, I think "fibration" ought to mean that one is
not dealing with the most general morphism but with a suitable morphism
such that the preimages can be thought of as being parametrized by the
base. To me, this means that you definitely want the morphism to be
surjective or at least dominant.
In algebraic geometry, a fibration needs not be equidimensional (or
''flat'' in the sense of commutative algebra). This is different from the
topologist's fibrations.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:22>
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