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The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings (2000)

Huber, Birkett ; Rambau, Jörg ; Santos, Francisco

Springer

Journal of the European Mathematical Society 2 (2000), S. 179-198

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Details

ISSN: 1435-9863

Schlagwort(e): Mathematics Subject Classification (1991): 52B11, 52B20, 14M25

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract. 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 ?1+...+? r of point configurations and of coherent polyhedral subdivisions of the associated Cayley embedding ?(?1,...,? 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 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s100970050003

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