Opened 10 years ago
Closed 9 years ago
#12361 closed defect (fixed)
Fix normalization in cohomology ring of orbifold toric varieties
Reported by: | vbraun | Owned by: | AlexGhitza |
---|---|---|---|
Priority: | major | Milestone: | sage-5.1 |
Component: | algebraic geometry | Keywords: | |
Cc: | novoselt, davideklund | Merged in: | sage-5.1.beta0 |
Authors: | Volker Braun | Reviewers: | David Eklund, Andrey Novoseltsev |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
For simplicial toric varieties, the rational cohomology ring and the ratironal Chow group are isomorphic. So if all normalizations are correct, then one should be able to do intersection computations in the cohomology ring. This patch fixes the volume_class()
and the constructor of cohomology cycles from cones to make everything work.
It turns out that index_in_saturation does not work for trivial zero-size matrices, this is also fixed.
Apply trac_12361_fix_toric_cohomology_ring.patch, trac_12361_index_in_saturation_fix.patch
Attachments (2)
Change History (17)
Changed 10 years ago by
comment:1 Changed 10 years ago by
- Cc novoselt added
- Description modified (diff)
- Status changed from new to needs_review
comment:2 Changed 9 years ago by
- Reviewers set to Andrey Novoseltsev
The patchbot complains about added whitespace! Looking at the actual code...
comment:3 Changed 9 years ago by
That's a really great expansion of the documentation!
I think I caught some typos:
- In
toric_variety
line 213 should be "many quantities of interest" without "s" on the end. - On line 1977 "It gets tricky none of the maximal cones is smooth." does not sound right, some words or punctuation sighs are missing.
comment:4 Changed 9 years ago by
- Status changed from needs_review to needs_work
- Work issues set to whitespaces and typos
OK, other than the above looks good!
comment:5 Changed 9 years ago by
Hi. I looked at this and I agree that it looks good.
One thing:
On line 215 of toric_variety.py it says "For toric varieties with at most orbifold singularities, the rational cohomology ring H(X,\QQ)
and the rational Chow ring H(X,\QQ)
are isomorphic."
It's a bit confusing that they are both denoted by H(X,\QQ). Maybe A(X,\QQ) could be used for the Chow ring. Or H^*(X,\QQ)
for cohomology and H_*(X,\QQ)
for the Chow ring (if intersection homology and the Chow ring were already identified somehow).
comment:6 Changed 9 years ago by
- Cc davideklund added
comment:7 Changed 9 years ago by
Oh yes good catch I meant to write A(X,\QQ)
of course.
comment:9 Changed 9 years ago by
- Reviewers changed from Andrey Novoseltsev to David Eklund, Andrey Novoseltsev
- Status changed from needs_review to needs_work
Comments 2&3 are still applicable and the patchbot complains ;-)
comment:10 Changed 9 years ago by
I've improved the docstrings.
As for the whitespace, I think this is a non-issue. There was some discussion on sage-devel and the consensus seems to be that its not worth the effort. Its a button press away (either with emacs or with the mercurial checkfiles plugin) to strip all trailing whitespace, but that would just break every patch we currently have. Mercurial tells me that there are 170 places in toric_varieties.py with superfluous spaces, so a few more or less doesn't matter. I'd rather not spend an hour fixing all patches that I currently have just to make the whitespace plugin happy.
comment:11 Changed 9 years ago by
- Status changed from needs_work to needs_review
comment:12 Changed 9 years ago by
- Status changed from needs_review to positive_review
comment:13 Changed 9 years ago by
- Work issues whitespaces and typos deleted
comment:14 Changed 9 years ago by
- Description modified (diff)
- Milestone changed from sage-5.0 to sage-5.1
comment:15 Changed 9 years ago by
- Merged in set to sage-5.1.beta0
- Resolution set to fixed
- Status changed from positive_review to closed
Initial patch