#8989: Add support for Fano toric varieties
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Reporter: novoselt | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.5
Component: algebraic geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by vbraun):
So just to get this straight, there will be a `CompleteIntersection` class
(to be implemented in the future) analogous to the already-implemented
`AnticanonicalHypersurface`. Only `CompleteIntersection` will know about
the nef partition, but not the ambient `CPRFanoToricVariety_field`.
Then, there will be methods (perhaps with `_star` instead of `_polar`)
{{{
CI.Delta(i), i=1..r
CI.nabla(i), i=1..r
CI.Delta() = convex hull( CI.Delta(i) )
CI.Delta_polar() = Minkowski sum( CI.nabla(i) )
CI.nabla() = convex hull( CI.nabla(i) )
CI.nabla_polar(j) = Minkowski sum( CI.Delta(i) )
}}}
for the usual polytopology of nef partitions. The only relations to the
polytopes of the ambient toric variety are
{{{
cpr_fano.Delta() == CI.Delta()
cpr_fano.Delta_polar() == CI.Delta_polar()
}}}
That would be fine with me. A `Delta_polar_to_coordinate` method is ok,
too.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8989#comment:16>
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