#16334: Toric divisors from fans in sublattices
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Reporter: jkeitel | Owner:
Type: defect | Status:
Priority: major | needs_review
Component: algebraic geometry | Milestone: sage-6.3
Keywords: toric | Resolution:
Authors: Jan Keitel | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
u/jkeitel/toric_divisor_sublattice | Commit:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Jan Keitel', 'oldvalue': ''}):
* status: new => needs_review
* branch: => u/jkeitel/toric_divisor_sublattice
* author: => Jan Keitel
Old description:
> Currently, there's a problem with toric divisors of toric varieties
> created from fans that live in a sublattice.
>
> The following examples illustrates that:
> {{{
> sage: N = ToricLattice(3)
> sage: S = N.submodule([(1,0,0), (0, 1, 0)])
> sage: B = S.basis()
> sage: cones = [Cone([B[0], B[1]]), Cone([B[1], -B[0]-B[1]]),
> Cone([-B[0]-B[1], B[0]])]
> sage: f = Fan(cones)
> sage: X = ToricVariety(f)
> sage: X.is_complete()
> True
> sage: (-X.K()).polyhedron()
> A 3-dimensional polyhedron in QQ^3 defined as the convex hull of 3
> vertices and 1 line
> }}}
> However, the real polyhedron should be a two-dimensional compact polygon:
> {{{
> sage: (-toric_varieties.P(2).K()).polyhedron()
> A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 3
> vertices
> }}}
>
> I'll attach a branch with a fix soon.
New description:
Currently, there's a problem with toric divisors of toric varieties
created from fans that live in a sublattice.
The following examples illustrates that:
{{{
sage: N = ToricLattice(3)
sage: S = N.submodule([(1,0,0), (0, 1, 0)])
sage: B = S.basis()
sage: cones = [Cone([B[0], B[1]]), Cone([B[1], -B[0]-B[1]]),
Cone([-B[0]-B[1], B[0]])]
sage: f = Fan(cones)
sage: X = ToricVariety(f)
sage: X.is_complete()
True
sage: (-X.K()).polyhedron()
A 3-dimensional polyhedron in QQ^3 defined as the convex hull of 3
vertices and 1 line
}}}
However, the real polyhedron should be a two-dimensional compact polygon:
{{{
sage: (-toric_varieties.P(2).K()).polyhedron()
A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 3
vertices
}}}
--
Comment:
Alright, here's a short patch that fixes the problem. I don't know whether
it's the best way of working around this, but it's simple and does the
trick.
Volker, could you have a look? :)
--
Ticket URL: <http://trac.sagemath.org/ticket/16334#comment:2>
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