#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.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12892#comment:18>
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