Triangulations and Secondary Polytopes

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


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.


Convex Hull Normal Cone Face Lattice Convex Polytope Affine Relation 
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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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