Combinatorial Convexity and Algebraic Geom...

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Beschreibung

The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts.

Inhaltsverzeichnis

1 Combinatorial Convexity.- I. Convex Bodies.- II. Combinatorial theory of polytopes and polyhedral sets.- III. Polyhedral spheres.- IV. Minkowski sum and mixed volume.- V. Lattice polytopes and fans.- 2 Algebraic Geometry.- VI. Toric varieties.- VII. Sheaves and projective toric varieties.- VIII. Cohomology of toric varieties.- Appendix Comments, historical notes, further exercises, research problems, suggestions for further reading.- References.- List of Symbols.

Erscheinungsjahr:	2011
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 374 S.
ISBN-13:	9781461284765
ISBN-10:	1461284767
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Ewald, Günter
Auflage:	Softcover reprint of the original 1st edition 1996
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 22 mm
Von/Mit:	Günter Ewald
Erscheinungsdatum:	17.09.2011
Gewicht:	0,593 kg

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