#11385: Orbit closure as toric variety
------------------------------------------------+---------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: algebraic geometry | Keywords: sd31
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev, Volker Braun | Author: Volker
Braun, Andrey Novoseltsev
Merged: | Dependencies:
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Changes (by newvalueoldvalue):
* reviewer: Andrey Novoseltsev => Andrey Novoseltsev, Volker Braun
* author: Volker Braun => Volker Braun, Andrey Novoseltsev
Old description:
> The closure of the torus orbit associated to a cone of the fan is again a
> toric variety. This patch implements a method
> `toric_variety.orbit_closure(cone)` to construct this toric variety.
New description:
The closure of the torus orbit associated to a cone of the fan is again a
toric variety. This patch implements a method
`toric_variety.orbit_closure(cone)` to construct this toric variety.
'''Apply:'''
1. [attachment:trac_11385_orbit_closure_as_toric_variety.patch]
1. [attachment:trac_11385_reviewer.patch]
--
Comment:
Ideally the toric variety of the orbit closure should come with the
canonical embedding, even though it does not come from a fan morphism. So
I think it would be better to have the restriction directly in the toric
variety class.
The attached patch contains bits of code that move us closer to supporting
quotient lattices, so I propose to add them - I wrote them while making
the commented code work. It still does not work for cones, so I agree to
leave the rest of necessary changes for the future. I also changed the
docstrings quite a bit, hopefully for the best ;-)
If you are OK with the new stuff, please switch to positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11385#comment:9>
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