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Chow polytopes and general resultants. (English) Zbl 0780.14027
The paper studies combinatoric properties of an algebraic variety \(X\), embedded in a projective space \(\mathbb{P}^ n\), relative to a distinguished coordinate frame. Let \(T\) be the maximal torus of \(GL(n+1)\) associated to the coordinate frame. The authors consider as a toric variety the closure of the \(T\)-orbit of the point representing \(X\) in the Chow variety. The polytope associated to such a projective toric variety is called the Chow polytope of \(X\): it gives a description of the toric degenerations of \(X\) and it is related to other polytopes already associated to \(X\) (state polytopes). The case of \(X\) itself being a toric variety is also considered.

MSC:
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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