#14353: Factor toric morphism into surjective and generically injective
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: algebraic geometry | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Volker Braun | Merged in:
Dependencies: | Stopgaps:
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Comment (by vbraun):
I don't think there are particularly good names for the intermediate fans.
Instead of trying to invent some name, we can just let a user use
`domain_fan()` / `image_fan()` on the factored morphism.
We have a choice for `Sigma_i`. Just the intersection with the image
sublattice will in general contain cones whose preimage under `f_b` is
empty. We can leave those out and get a smaller `Sigma_i`. E.g. take the
composition of the half blowup chart with the embedding `C^2-> P^2`. The
natural thing to do is probably take this smaller fan. So `f_i` would be
the embedding `C^2->P^2` in the example.
I'm happy to get rid of `restrict_to_image`, I was tempted to do that
myself....
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14353#comment:5>
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