#9326: Add cohomology of toric varieties
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.5.1
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by vbraun):
3. I was trying to not have yet another ring attached to fans, since there
are already too many rings floating around ;-) On the other hand, the SR
ideal makes sense just for fans so I wanted to move the SR ideal function
there, maybe someone is interested in it without the toric variety. I'll
move the caching of rings up to the toric variety.
4. I agree with the divisor names, but until we have the divisors finished
I think its easiest to just go with default names = names of homogeneous
coordinates.
12. Integration is with compact supports (it is really intersection in
homology)
{{{
sage: C2 = toric_varieties.A2()
sage: C2.volume_form()
0
}}}
and the index theorem doesn't work. In particular, Euler number of `C^2` =
Euler number of point = 1. And yes, evaluation of the index theorem is
faster than computing a basis for the (co)homology groups.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9326#comment:14>
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