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The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings. (English) Zbl 0988.52017
B. Sturmfels [J. Algebr. Comb. 3, No. 2, 207-236 (1994; Zbl 0798.05074)] has established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum of point configurations in $$\mathbb R^d$$ and of coherent polyhedral subdivisions of the associated Cayley embedding – the polyhedral version of the Cayley trick of elimination theory. The authors generalize this relationship in the case of non-coherent subdivisions. As an application, a new proof is given of the Bohne-Dress theorem on zonotopal tilings.
Reviewer: Eike Hertel (Jena)

##### MSC:
 52B11 $$n$$-dimensional polytopes 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
##### Keywords:
polytopes; subdivision; zonotopal tiling
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