#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):
There were failures due to the switch to `PointCollection`, I've fixed
them (added `__add__`).
How about the following?
* `fiber_generic()` returns (X, N) where X is a toric variety
corresponding to the kernel fan and N is the number of copies if the whole
torus of the codomain is covered surjectively and 0 otherwise.
* `fiber_component(domain_cone)` returns (X, N) where N is always some
positive number of copies, since here we specify a domain cone and there
are definitely some components corresponding to it, in particular
`fiber_component(domain_origin)` will return the number of components of
the fiber over distinguished point of the `codomain_origin`, even if
`fiber_generic` returns (X, 0), meaning that over non-distinguished points
there are likely empty fibers.
* `fiber_dimension(codomain_cone)` returns -1 (or -intinity?) if the
corresponding orbit of the codomain is not covered surjectively.
* `fiber_graph(codomain_cone)` returns an empty graph is the
corresponding orbit is not covered surjectively.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:18>
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