#10325: Cohomology Ring of toric varieties not unique
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Reporter: vbraun | Owner: AlexGhitza
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.6.2
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Changes (by novoselt):
* status: needs_review => positive_review
* reviewer: => Andrey Novoseltsev
Comment:
I really really don't like this:
{{{
sage: X2.toric_divisor_group().scheme() is X2
False
}}}
It seems to me that either schemes must be unique as well, or their
divisor groups should be separate. I think that the second option makes
more sense since schemes are "the main ones" and divisor groups
automatically will be unique if their schemes decide to be uniqie.
However this is not the problem of toric varieties only, other schemes are
also non-unique while divisor groups are. In the long run it should be
taken care of, but for now the attached patch offers a partial solution
and I don't think that it creates any new problems. So positive review,
I'll open a new ticket for the bigger problem.
As I concluded from some discussions on sage-combinat, `FormalSum` which
is used as a base for divisor groups should eventually be deprecated as
`CombinatorialFreeModule` is the new way to go. Perhaps sometime we can do
the switch and free derived objects from uniqueness decisions.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10325#comment:2>
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