#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 novoselt):
3. Well, if SR ideal does make sense for fans, then, since it is an ideal,
it lives in some ring. What is this ring? (And in what situations does it
come up?) It just seems to me that if this ring is not canonically
associated to the fan, then it means that both the ring and the ideal
actually correspond to some object derived from the fan, rather than fan
itself. If this is the case and you still really want to have it as a
method of a fan, then I think that the ring argument must be mandatory.
4. OK, let's leave this for later (I'd actually prefer to play with it a
bit before choosing a default name scheme).
11-12. I find this example quite confusing for a new user. The plane has
zero volume form? What about `dx\wedge dy`??? We go to
http://en.wikipedia.org/wiki/Volume_form and see that any orientable
Riemannian manifold has infinitely many volume forms, and they are never
0. Can we maybe rename it to `volume_class` or something? That's how other
functions returning cohomology classes are named. By the way, calling it
for a non-simplicial variety (e.g. `Cube_face_fan`) crashes with a non-
informative message in the context of toric varieties: "self must be a
square matrix."
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9326#comment:15>
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