#9963: non-nef divisors can have sections, too
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Reporter: vbraun | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by vbraun):
* status: new => needs_review
Old description:
> `ToricDivisor_generic.sections()` has an incorrect shortcut if the
> divisor is not nef. The cohomology of the divisor is computed correctly:
> {{{
> sage: rays =
> [(1,0,0),(0,1,0),(0,0,1),(-2,0,-1),(-2,-1,0),(-3,-1,-1),(1,1,1),(-1,0,0)]
> sage: cones =
> [[0,1,3],[0,1,6],[0,2,4],[0,2,6],[0,3,5],[0,4,5],[1,3,7],[1,6,7],[2,4,7],[2,6,7],[3,5,7],[4,5,7]]
> sage: X = ToricVariety(Fan(rays=rays,cones=cones))
> sage: D = X.divisor(2); D
> V(z2)
> sage: D.is_nef()
> False
> sage: D.sections()
> ()
> sage: D.cohomology(dim=True)
> (1, 0, 0, 0)
> }}}
> Attached one-line patch fixes this issue and adds doctest.
New description:
`ToricDivisor_generic.sections()` has an incorrect shortcut if the divisor
is not nef. The cohomology of the divisor is computed correctly:
{{{
sage: rays =
[(1,0,0),(0,1,0),(0,0,1),(-2,0,-1),(-2,-1,0),(-3,-1,-1),(1,1,1),(-1,0,0)]
sage: cones =
[[0,1,3],[0,1,6],[0,2,4],[0,2,6],[0,3,5],[0,4,5],[1,3,7],[1,6,7],[2,4,7],[2,6,7],[3,5,7],[4,5,7]]
sage: X = ToricVariety(Fan(rays=rays,cones=cones))
sage: D = X.divisor(2); D
V(z2)
sage: D.is_nef()
False
sage: D.sections()
()
sage: D.cohomology(dim=True)
(1, 0, 0, 0)
}}}
Attached one-line patch fixes this issue and adds doctest.
See tracker bug at #9604 to for the patch queue/dependencies.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9963#comment:1>
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