#18443: Multiplier spectra for projective morphisms
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.8
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Ben Hutz
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3333f6a4115954aa3a5e3e209e35e8b104ac160a
u/gjorgenson/ticket/18443 | Stopgaps:
Dependencies: #18409 |
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Changes (by bhutz):
* status: needs_review => needs_work
Comment:
A couple things in multiplier_spectrum
- you should check that the domain is projective space to avoid subschemes
- K = f._number_field_from_algebraics() should be outside the if
- if [1,0] is a point of multplicity you will miss this (You also only
check if it is fixed not n-periodic). You could instead see if the poly F
is of the form `y^m*G(x,y)` for some poly G, then m is the multplicity of
[1,0].
- it doesn't seem like your conversion to QQbar is working. Trying your
number field example, when the map is actually defined over a number field
{{{
sage: set_verbose(None)
sage: z = QQ['z'].0
sage: K.<w> = NumberField(z^4 - 4*z^2 + 1)
sage: P.<x,y> = ProjectiveSpace(K,1)
sage: H = End(P)
sage: f = H([x^2 - w/4*y^2,y^2])
sage: f.multiplier_spectra(2,False)
}}}
Not sure exactly what you should do here. One option is to get change_ring
for polynomials to deal with QQbar, by passing in and/or creating an
embedding. If you look in
schemes.generic.morphism.SchemeMorphism_polynomial.change_ring() it gives
a simple way to construct a hom of polynomials given a hom of the base
rings. It does appear that the change_ring of the parent is working, so
you probably just need to create the hom between the poly rings and apply
it to the element to be changed.
--
Ticket URL: <http://trac.sagemath.org/ticket/18443#comment:8>
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