Combinatorial convexity and algebraic geometry
Series: Graduate Texts in Mathematics; Vol.168Publication details: Springer, 1996 New York:Description: xiv; 372p. pb; 24 cmISBN:- 9781461284765
- 511.6 EWA
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IIT Gandhinagar General Stacks | 511.6 EWA (Browse shelf(Opens below)) | 1 | Available | 028474 |
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511.5 TER Zeta functions of graphs: a stroll through the garden | 511.54 MOO Topics on tournaments in graph theory | 511.6 BAI Association schemes: designed experiments, algebra and combinatorics | 511.6 EWA Combinatorial convexity and algebraic geometry | 511.6 GOR Matroids: a geometric introduction | 511.6 OXL Matroid theory | 511.6 PEM Analytic combinatorics in several variables |
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.
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