#10882: Add kernel fan to fan morphism
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: geometry | Keywords: toric geometry
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: | Merged:
Work_issues: degenerate cases |
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Changes (by novoselt):
* status: new => needs_work
* work_issues: => degenerate cases
Comment:
Hi Volker,
The patch is quite easy, as `preimage_cones` were already implemented, but
in order to make everything shiny it would be nice to improve handling of
degenerate cases. For this I need to resolve the situation with trivial
fans, namely: is an empty set a fan, or it must include at least the
origin? Fulton and Cox-Little-Schenck don't mention it explicitly, but
from the point of view of nice correspondence to toric varieties it seems
that completely empty fans should be prohibited as they seem to correspond
to empty varieties, but then they don't really contain a torus.
Right now it is possible in Sage to create a fan without cones, I propose
to automatically add the origin of the provided lattice in this case and
treat it as the generating cone. Any objections?
Regarding `preimage_fans(cone)` it would imply that usually it is
generated by `preimage_cones(cone)`, but some of them maybe unnecessary
for generation (e.g. in the case of blow-up, described in the
documentation), i.e. generating cones of `preimage_fan(cone)` are a subset
of `preimage_cones(cone)`. However, if `preimage_cones(cone)` is empty,
then `preimage_fan(cone)` will have an "extra" generating cone, namely the
origin.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10882#comment:1>
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