#9713: Add toric Chow group
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: coordinate order of components |
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Comment(by kcrisman):
Replying to [comment:12 vbraun]:
> The '''toric''' Chow cycles are the torus-invariant subvarieties only.
Yes, I got that.
> Its a standard construction, see e.g. Fultons book. I don't think that
there is any hope of it being the same as the full Chow group.
Ah, when you say "Fulton's book" I first got out Intersection Theory :)
but here it is. Sections 3.3 and 3.4 seem quite relevant. Page 63 says
that Pic and the divisor piece of the Chow group can be computed only with
what Fulton consistently calls "T-Weil" and "T-Cartier" divisors.
Further, the first proposition in Chapter 5 certainly seems to imply that
this is in fact true in general for toric varieties. The 'orbit closures'
seem to be toric subvarieties by definition, and they generate the Chow
group. Am I reading this wrong?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9713#comment:13>
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