<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>387</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-01-28</completedDate>
    <publishedDate>1999-01-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings</title>
    <abstract language="eng">In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of \emph{coherent} mixed subdivisions of a Minkowski sum $\mathcal{A}_1+\cdots+\mathcal{A}_r$ of point configurations and of \emph{coherent} polyhedral subdivisions of the associated Cayley embedding $\mathcal{C}(\mathcal{A}_1,\dots,\mathcal{A}_r)$. In this paper we extend this correspondence in a natural way to cover also \emph{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.</abstract>
    <identifier type="serial">SC-98-44</identifier>
    <identifier type="opus3-id">388</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3874</identifier>
    <enrichment key="SourceTitle">Appeared in: "The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings", Journal of the European Mathematical Society, 2 (2000) 179-198</enrichment>
    <author>Birkett Huber</author>
    <author>Jörg Rambau</author>
    <author>Francisco Santos</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-44</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Polyhedral subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>fiber polytope</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mixed subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lifting subdivision</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Minkowski sum</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cayley Trick</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bohne-Dress Theorem</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="14M25">Toric varieties, Newton polyhedra [See also 52B20]</collection>
    <collection role="msc" number="52B11">n-dimensional polytopes</collection>
    <collection role="msc" number="52B20">Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="projects" number="ZIB-PolSub">ZIB-PolSub</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/387/SC-98-44.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/387/SC-98-44.pdf</file>
  </doc>
</export-example>
