On Wed, May 19, 2010 at 2:17 AM, Volker Braun <vbraun.n...@gmail.com> wrote:
> Hi Andrey,
>
> I agree that the reflexive case is the most interesting, I just don't
> understand where you need that in the FanoToricVariety code right now.
> If we can relax restrictions without any cost then we should allow the
> more general, right? On the other hand, if it would make the code more
> complicated then screw it...
>
Hi Volker,
All resolutions are currently automatically crepant because reflexive
polytopes just don't have other points (except the origin). General
polytopes will require more care. Anticanonical hypersurface relies on
reflexivity for terminology, it is CY, and I don't think that the code
will produce the right divisor for non-reflexive polytopes. And, as I
said, the hope is to add more reflexive-specific code later. E.g.
generating function for Hodge numbers or direct use of combinatorial
formulas to compute Hodge numbers.
> On May 19, 4:03 am, Andrey Novoseltsev <novos...@gmail.com> wrote:
>> [...] we can add "PCR" in
>> the beginning or the end (corresponding to PartialCrepantResolution).
>
> Batyrev already defined the abbreviation
>
> MPCP resolution =
> (maximal projective crepant partial) resolution =
> maximal subdivision of polyhedron
>
> I think you want to do everything except the "maximal" (and perhaps
> except the "projective", I don't see why you need to enforce that in
> the Sage class), so how about PCPR or CPR? CPRFanoToricVariety_field?
>
CPR is perfect! I definitely don't want to have maximal and I'd rather
not have projective as it is harder to implement.
>> [...] How
>> about also latexing them with subscripts? Like "(1,2)_{N}"?
>
> Nice!
>
>> One way or another they will have to define variables containing the
>> lattices, but that's pretty much unavoidable, I don't think it is a
>> good idea to put names like "N" and "M" into the global name space.
>
> In fact, "N" is already in the global workspace :-)
>
> sage: N(1/2)
> 0.500000000000000
>
Wow... Well, at least it does something widely used ;-)
> Are you implementing the ToricLattice soon? Clearly this should be
> done first...
Yes, I just got this week very busy with other stuff. Hope to start on
the weekend.
Have to run now, will reply to your second message later (I even need
to read it first).
Thank you,
Andrey
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