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Triangulations and Secondary Polytopes

  • Israel M. Gelfand
  • Mikhail M. Kapranov
  • Andrei V. Zelevinsky
Part of the Mathematics: Theory & Applications book series (MBC)

Abstract

In this chapter we discuss a combinatorial framework for discriminants and resultants related to toric varieties. The main construction introduces a certain class of polytopes, called secondary polytopes, whose vertices correspond to certain triangulations of a given convex polytope. These polytopes will play a crucial role later in the study of the Newton polytopes of discriminants and resultants. The constructions in this chapter are quite elementary.

Keywords

Convex Hull Normal Cone Face Lattice Convex Polytope Affine Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Israel M. Gelfand
    • 1
  • Mikhail M. Kapranov
    • 2
  • Andrei V. Zelevinsky
    • 3
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsNortheastern UniversityBostonUSA

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