Geodesic
The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings
Journal of the European Mathematical Society, Tome 2 (2000) no. 2, pp. 179-198.

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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 A1​+⋯+Ar​ of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding C(A,​...,Ar​). 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 of Lawrence polytopes provides a new independent proof of the Bohne–Dress theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos.
DOI : 10.1007/s100970050003
Classification : 00-XX 
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     author = {Birkett Huber and J\"org Rambau and Francisco Santos},
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Birkett Huber; Jörg Rambau; Francisco Santos. The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings. Journal of the European Mathematical Society, Tome 2 (2000) no. 2, pp. 179-198. doi : 10.1007/s100970050003. http://geodesic.mathdoc.fr/articles/10.1007/s100970050003/

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