#10540: Spec and patches for singular affine toric varieties / algebraic schemes
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords:
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev | Author: Volker Braun
Merged: | Dependencies: #9918, #10525, #10023,
#10529
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Comment(by vbraun):
5. (line 433) In some (singular) cases you can't express the
embedding morphism as polynomial map, so it currently can't be
represented in Sage. The embedding morphism is constructed as a
byproduct of the patch, so we can't immediately raise an
exception. Really, we only need the patch and the pull-back of
ideals and never the embedding morphism.
6. (line 441) You are right, I changed it to `embedding_center`.
7. (line 1847) fixed.
8. (line 1859) fixed.
9. (line 2076) I removed the `toric_algebraic_patch()` which was an
alias for `affine_patch()`.
For projective space, `affine_patch()` returns the cover by
affine space. The natural analog for toric varieties is the cover
by an affine toric variety, and is again called
`affine_patch()`. There is also a useful patch covering by an
affine algebraic variety, which I called
`affine_algebraic_patch`. I do want to distinguish `affine_patch`
and `affine_algebraic_patch` since they produce very different
output.
10. (line 2169) I added an extra line to filter out the 0 generator to the
ideal, though mathematically it of course makes no difference.
11. (line 2193) thanks for reminding me :-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10540#comment:10>
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