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INICIO | 16 de abril de 2024
  

On the refinements of a polyhedral subdivision.

Título inglés On the refinements of a polyhedral subdivision.
Título español Refinamientos de una subdivisión poliedral.
Autor/es Santos, Francisco
Organización Dep. Mat. Estad. Comput. Univ. Cantabria, Santander, España
Revista 0010-0757
Publicación 2001, 52 (3): 231-256, 26 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced subdivision. In particular, we define the refinement polytope associated to any pi-induced subdivision S, which is a generalization of the fiber polytope and shares most of its properties. As applications to the theory we prove that if a point configuration has non-regular subdivisions then it has non-regular triangulations and we provide simple proofs of the existence of non-regular subdivisions for many particular point configurations.
Clasificación UNESCO 120410
Palabras clave español Geometría proyectiva ; Politopos ; Refinamiento ; Poliedro
Código MathReviews MR1885221
Código Z-Math Zbl 1012.52018
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es