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:

Status badges

Description (last modified by jdemeyer)

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)

trac_12361_index_in_saturation_fix.patch (1.5 KB) - added by vbraun 10 years ago.
Initial patch
trac_12361_fix_toric_cohomology_ring.patch (21.1 KB) - added by vbraun 9 years ago.
Updated patch

Download all attachments as: .zip

Change History (17)

Changed 10 years ago by vbraun

Initial patch

comment:1 Changed 10 years ago by vbraun

  • Cc novoselt added
  • Description modified (diff)
  • Status changed from new to needs_review

comment:2 Changed 9 years ago by novoselt

  • Reviewers set to Andrey Novoseltsev

The patchbot complains about added whitespace! Looking at the actual code...

comment:3 Changed 9 years ago by novoselt

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 novoselt

  • 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 davideklund

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 davideklund

  • Cc davideklund added

comment:7 Changed 9 years ago by vbraun

Oh yes good catch I meant to write A(X,\QQ) of course.

comment:8 Changed 9 years ago by vbraun

  • Status changed from needs_work to needs_review

Fixed!

comment:9 Changed 9 years ago by novoselt

  • 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 ;-)

Changed 9 years ago by vbraun

Updated patch

comment:10 Changed 9 years ago by vbraun

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 vbraun

  • Status changed from needs_work to needs_review

comment:12 Changed 9 years ago by novoselt

  • Status changed from needs_review to positive_review

comment:13 Changed 9 years ago by novoselt

  • Work issues whitespaces and typos deleted

comment:14 Changed 9 years ago by jdemeyer

  • Description modified (diff)
  • Milestone changed from sage-5.0 to sage-5.1

comment:15 Changed 9 years ago by jdemeyer

  • Merged in set to sage-5.1.beta0
  • Resolution set to fixed
  • Status changed from positive_review to closed
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