Opened 9 years ago
Closed 8 years ago
#13084 closed enhancement (fixed)
Weierstrass form for toric elliptic curves
Reported by: | vbraun | Owned by: | AlexGhitza |
---|---|---|---|
Priority: | major | Milestone: | sage-5.11 |
Component: | algebraic geometry | Keywords: | |
Cc: | novoselt, dimpase, mstreng | Merged in: | sage-5.11.beta2 |
Authors: | Volker Braun | Reviewers: | Frédéric Chapoton, Dmitrii Pasechnik |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #12553, #13451 | Stopgaps: |
Description (last modified by )
This ticket implements the Weierstrass form (of the Jacobian) of anticanonical hypersurfaces in toric surfaces defined by reflexive polygons:
sage: from sage.schemes.toric.weierstrass import WeierstrassForm sage: R.<x,y> = QQ[] sage: cubic = x^3 + y^3 + 1 sage: WeierstrassForm(cubic) # cubic in P^2 (0, -27/4) sage: WeierstrassForm(x^4 + y^2 + 1) # in P^2[112] (-4, 0) sage: WeierstrassForm(x^2*y^2 + x^2 + y^2 + 1) # in P^1xP^1 (-16/3, 128/27)
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Attachments (5)
Change History (33)
comment:1 Changed 9 years ago by
- Cc novoselt added
- Dependencies set to #12553
- Description modified (diff)
- Status changed from new to needs_review
comment:2 Changed 9 years ago by
comment:3 Changed 9 years ago by
The reference looks interesting, I'll have a look!
Though I think there is already too much code in this ticket, any further features should go to a followup.
comment:4 Changed 9 years ago by
- Dependencies changed from #12553 to #12553, #13451
I've split off the classical invariant theory stuff into a different module (#13451), this is much cleaner now. Still needs review ;-)
comment:5 Changed 8 years ago by
apply only trac_13084_toric_weierstrass.patch
comment:6 Changed 8 years ago by
- Description modified (diff)
comment:7 Changed 8 years ago by
rediffed for sage-5.8.beta0
comment:8 follow-up: ↓ 9 Changed 8 years ago by
- Cc dimpase added
This is mostly geometry of polygons with a little bit of invariant theory thrown in - Dima, do you feel comfortable reviewing the ticket?
comment:9 in reply to: ↑ 8 Changed 8 years ago by
Replying to vbraun:
This is mostly geometry of polygons with a little bit of invariant theory thrown in - Dima, do you feel comfortable reviewing the ticket?
This is surely a fun ticket!
But I am not familiar with the number theory part of it, and lately falling behind with everything, including reviewing my son's nappy's :–) Besides, it ought to be reviewed by number theorists.
Let me in turn invite you to consider taking part in this: http://web.spms.ntu.edu.sg/~dima/IMS2013/
comment:10 Changed 8 years ago by
- Cc mstreng added
For the record, there isn't really any number theory in here. Maybe Marco is interested in reviewing this? ;-)
comment:11 Changed 8 years ago by
- Status changed from needs_review to needs_work
- Work issues set to coverage, doctest
See the bot report:
- coverage is not 100%
- needs to use the new doctest continuation
...:
comment:12 Changed 8 years ago by
Fixed
comment:13 Changed 8 years ago by
- Status changed from needs_work to needs_review
comment:14 Changed 8 years ago by
Frédéric, are you going to review this ticket?
comment:15 Changed 8 years ago by
I have added a "cosmetic cleanup" patch for the file weierstrass.py. In particular, it removes many unused import statements.
comment:16 Changed 8 years ago by
Thanks, looks good to me.
Changed 8 years ago by
comment:17 Changed 8 years ago by
- Description modified (diff)
Another cosmetic-cleanup patch. Similar work on import statements and pep8
Changed 8 years ago by
comment:18 Changed 8 years ago by
Looks good to me.
I take it you forgot to set the ticket to positive review after posting patches for all of the new code?
comment:19 Changed 8 years ago by
well, I am not able to seriously review the math..
comment:20 follow-up: ↓ 21 Changed 8 years ago by
Attempting to look at the maths side. It's confusing that you start off talking about a toric elliptic curve, but then speak about "the elliptic curve". What is going on there?
further nitpicks:
There are 16 reflexive polygons in 2-d.
Could you add a reference and change this to
There are 16 reflexive polygons in the plane.
And add an exact reference to the next statement.
Each defines a toric fano variety, which (in 2-d) has a unique crepant resolution to a smooth toric surface.
Which should also be changed to
Each of them defines a toric Fano variety...
Then,
It turns out that the anticanonical hypersurface equation...
Reference?
comment:21 in reply to: ↑ 20 Changed 8 years ago by
Replying to dimpase:
And add an exact reference to the next statement.
Each defines a toric fano variety, which (in 2-d) has a unique crepant resolution to a smooth toric surface.
Thats just the fact that a fan in the plane has a unique refinement into smooth cones. CLS just say that "its easy to see" (p. 500)
comment:23 in reply to: ↑ 22 Changed 8 years ago by
comment:24 Changed 8 years ago by
- Status changed from needs_review to positive_review
hope you will update the relevant patch to change fano
to Fano
in docstrings...
comment:25 Changed 8 years ago by
Thanks, I fixed the "Fano".
Speaking of, its been grinding my gears the last couple of days that hilbert_series
is lower case in Sage ;-)
comment:26 Changed 8 years ago by
- Milestone changed from sage-5.10 to sage-5.11
- Reviewers set to Dmitrii Pasechnik
- Work issues coverage, doctest deleted
comment:27 Changed 8 years ago by
- Reviewers changed from Dmitrii Pasechnik to Frédéric Chapoton, Dmitrii Pasechnik
comment:28 Changed 8 years ago by
- Merged in set to sage-5.11.beta2
- Resolution set to fixed
- Status changed from positive_review to closed
Excellent work! In all these cases, the genus 1 curve is a cover of its jacobian in a relatively canonical way. With your approach, is it reasonably possible to compute these covering maps? Doing so gives a kind of "certificate". One starting point would be
also on arXiv.