#15113: Implement computations in picard groups via global sections of line
bundles
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Reporter: nbruin | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.12
Component: algebraic geometry | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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In a bunch of papers, Kamal Khuri Makdisi outlines how standard techniques
to compute with coherent sheafs via global sections of their twists can be
used to obtain (at least asymptotically) efficient algorthims to compute
in the Picard group of an algebraic curve (he outlines `Pic^0`, but the
ideas readily generalize to all of Pic).
A little experimentation shows that these techniques can be fairly
efficient in practice as well (and certainly usable!). We'll have to see
if the method can be truly competitive with the Hess-type "function field
as finite extension of k(x)" approach.
In any case, Kamal's approach is much easier to implement and, thanks to
its uniformity, much easier to trust, so at least as a stepping stone,
it's useful to have an implementation available.
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Ticket URL: <http://trac.sagemath.org/ticket/15113>
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