Existence of Unimodular Triangulations–Positive Results

Released on by Christian Haase
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  • Existence of Unimodular Triangulations–Positive Results Book Detail

  • Author : Christian Haase
  • Release Date : 2021-07-21
  • Publisher : American Mathematical Soc.
  • Genre : Education
  • Pages : 83
  • ISBN 13 : 1470447169
  • File Size : 66,66 MB
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Existence of Unimodular Triangulations–Positive Results by Christian Haase PDF Summary

Book Description: Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.

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Triangulations

Triangulations

File Size : 24,24 MB
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Triangulations presents the first comprehensive treatment of the theory of secondary polytopes and related topics. The text discusses the geometric structure be