Equimultiple liftings of curves over finite fields

[mminzlaff]

Let C be a plane projective curves over a finite field k and S a finite set of k-sections of the curve. It would be nice if Sage could compute a lifting of the plane curve to a p-adic ring R (with finite precision) and liftings of the k-sections to R-sections of the lifted curve such that the multiplicity of C at the i-th section is the same as the multplicity of the lifting at the lifted section.

Apply attachment: trac_13046_v3.patch

Depends on #12995

Component: algebraic geometry

Keywords: deformation theory, plane curves

Author: Moritz Minzlaff

Reviewer: William Stein, Max Leiblich

Issue created by migration from https://trac.sagemath.org/ticket/13046

[mminzlaff]

modifies the signature of the method

[mminzlaff]

comment:2

Attachment: trac_13046_inital.patch.gz

Apply trac_13046_v2.patch

[mminzlaff]

Attachment: trac_13046_v2.patch.gz

new version simplifies the signature/use of the method

[jdemeyer]

comment:5

Please add your real name as Author.

[mminzlaff]

Author: Moritz Minzlaff

[mminzlaff]

comment:6

Whoops. Done! :)

[williamstein]

comment:8

This needs to be rebased this against sage-5.12.rc3.

[williamstein]

Attachment: trac_13046_v3.patch.gz

rebased

[williamstein]

Reviewer: William Stein, Max Leiblich

[williamstein]

comment:9

Attached rebased.

[williamstein]

comment:10

REFEREE REPORT:

It looks good!

More precisely, I (William Stein) read the code for style, and Max Leiblich (an algebraic geometer) read the code for the mathematics, and we both agree it looks good.

Well, there is one unusual thing. There are backslashes in the comments so they occupy less than 80 characters, but when read, are wide. I've never seen this before anywhere in Sage/Python code. I'm not sure whether we should allow it or not. I'll leave this to the release manager.

[jdemeyer]

comment:12

I agree, the backslashes is a very strange thing, I wouldn't do that.

Also, never use

except:

without specifying an exception class, as it will catch stuff like KeyboardInterrupt.

[jdemeyer]

comment:13

Also, please use the new-style doctest continuations

sage:
....:
....:

[jdemeyer]

comment:14

Raising exceptions should be done in a Python 3 compatible way: raise TypeError("string") and you should add doctests for the exceptions also.