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The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings

Birkett Huber, Jörg Rambau, Francisco Santos (2000)

Journal of the European Mathematical Society

In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum 𝒜 1 + + 𝒜 r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding 𝒞 ( 𝒜 1 , , 𝒜 r ) . In this paper we extend this correspondence in a natural way to cover also non-coherent subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions...

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