#9326: Add cohomology of toric varieties
----------------------------------+-----------------------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Changes (by vbraun):
* status: needs_info => needs_review
Old description:
> This patch adds a cohomology ring to toric varieties. This is then used
> for characteristic classes.
>
> I'm using the usual description of the rational cohomology ring via the
> Stanley-Reisner ideal of the fan. This does not work for singular
> varities with worse than orbifold singularities. I don't have any good
> candidate for the "space where the Chern classes live" in that case.
>
> Prerequisites:
> * #9245: Add library of toric varieties.
> * #9429: Undesirable behaviour when deriving from `QuotientRingElement`
New description:
This patch adds a cohomology ring to toric varieties. This is then used
for characteristic classes.
I'm using the usual description of the rational cohomology ring via the
Stanley-Reisner ideal of the fan. This does not work for singular varities
with worse than orbifold singularities. I don't have any good candidate
for the "space where the Chern classes live" in that case.
Prerequisites:
* #9245: Add library of toric varieties.
--
Comment:
Updated patch that implements classes `CohomologyRing` and
`CohomologyClass`. These do not follow the coercion model since their
superclasses `QuotientRing_generic` and `QuotientRingElement` have not
been converted to the new coercion model. The new classes will easily
convert to the new coercion model once `QuotientRing` and its subclasses
are updated.
First apply `trac_9326_QuotientRing_fix_derived_classes.patch` (which is
just a renamed version of Andrey's
`trac_9429_fix_derived_classes.2.patch`), then
`trac_9326_toric_variety_cohomology.patch` on top.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9326#comment:11>
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