Existence of Unimodular Triangulations-Positive Results
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| Autore: |
Haase Christian
|
| Titolo: |
Existence of Unimodular Triangulations-Positive Results
|
| Pubblicazione: | Providence : , : American Mathematical Society, , 2021 |
| ©2021 | |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (96 pages) |
| Disciplina: | 516/.08 |
| Soggetto topico: | Convex polytopes |
| Triangularization (Mathematics) | |
| Combinatorial geometry | |
| Convex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry) | |
| Convex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopes | |
| Commutative algebra -- Arithmetic rings and other special rings -- Polynomial rings and ideals; rings of integer-valued polynomials | |
| Classificazione: | 52B2052B1113F20 |
| Altri autori: |
PaffenholzAndreas
PiechnikLindsay C
|
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | Cover -- Title page -- Chapter 1. Introduction -- 1.1. What? -- 1.2. Why? Who? -- 1.3. What is new? -- 1.4. What is not here -- 1.5. What is left? -- Chapter 2. Methods -- 2.1. Pulling Triangulations -- 2.2. Push-forward subdivisions and pull-back subdivisions -- 2.3. Joins and (Fiber) Products -- 2.4. Toric Gröbner Bases -- Chapter 3. Examples -- 3.1. Polytopes cut out by roots -- 3.2. Polytopes spanned by roots -- 3.3. Other Graph Polytopes -- 3.4. Lecture hall polytopes -- 3.5. Smooth Polytopes -- 3.6. The Gröbner fan and the toric Hilbert scheme -- Chapter 4. Dilations and the KMW Theorem -- 4.1. KMW numbers in dimension three -- 4.2. Canonical triangulation of a dilated simplex -- 4.3. Reducing the volume of simplices in the dilation -- 4.4. A proof of the KMW Theorem -- 4.5. An effective version of the KMW-Theorem -- Bibliography -- Back Cover. |
| Sommario/riassunto: | "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"-- |
| Titolo autorizzato: | Existence of Unimodular Triangulations-Positive Results |
| ISBN: | 9781470465308 |
| 1470465302 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910970826703321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society