#15239: Nondegeneracy for subschemes of toric varieties
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Reporter: vbraun | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Volker Braun | Work issues:
Report Upstream: N/A | Commit:
Branch: | f885028d7ab463ff6e870ffa1ff61558304a5986
u/vbraun/is_nondegenerate | Stopgaps:
Dependencies: |
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Changes (by ursula):
* status: needs_review => needs_work
Comment:
Compare Example 3.2.5 of Helmut A. Hamm, "Differential forms and Hodge
numbers for toric complete intersections" ( http://arxiv.org/abs/1106.1826
). That example gives a hypersurface that is not non-degenerate. It's
worked out in a patch, but I think the following test with a homogeneous
polynomial is equivalent:
{{{
X = toric_varieties.WP([1,4,2,3], names='z0 z1 z2 z3')
X.inject_variables()
g0 =z1^3 + z2^6 +z3^4
g = g0-2*z2^3*z0^6+z2*z0^10+z0^12
hyp = X.subscheme([g])
}}}
Right now, hyp.is_nondegenerate() returns True, but Hamm says it should
return False. The problem may be that the current code only checks at
top-dimensional cones, rather than checking at all cones in the fan?
--
Ticket URL: <http://trac.sagemath.org/ticket/15239#comment:6>
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