Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

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

Download PDF
20 pages

Loading next page...
 
/lp/springer-journals/the-cayley-trick-lifting-subdivisions-and-the-bohne-dress-theorem-on-UkHd1xuBfA
Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970050003
Publisher site
See Article on Publisher Site

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.

Journal

Journal of the European Mathematical Society – Springer Journals

Published: Jun 1, 2000

There are no references for this article.