Combinatorial Convexity And Algebraic Geometry
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Combinatorial Convexity And Algebraic Geometry
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Author : Guenter Ewald
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-10-03
Combinatorial Convexity And Algebraic Geometry written by Guenter Ewald and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-03 with Mathematics categories.
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Combinatorial Convexity And Algebraic Geometry
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Author : Günter Ewald
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial Convexity And Algebraic Geometry written by Günter Ewald and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Combinatorial Convexity And Algebraic Geometry
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Author : Günter Ewald
language : en
Publisher:
Release Date : 1997
Combinatorial Convexity And Algebraic Geometry written by Günter Ewald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Combinatorial Convexity And Algebraic Geometry
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Author : G. Ewald
language : en
Publisher:
Release Date : 1997
Combinatorial Convexity And Algebraic Geometry written by G. Ewald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Combinatorial Convexity
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Author : Imre Bárány
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-04
Combinatorial Convexity written by Imre Bárány and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-04 with Education categories.
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Combinatorial Convexity And Algebraic Geometry
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Author : Victor V. Batyrev
language : en
Publisher:
Release Date : 2001
Combinatorial Convexity And Algebraic Geometry written by Victor V. Batyrev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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Author : Takayuki Hibi
language : en
Publisher: World Scientific
Release Date : 2019-05-30
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes written by Takayuki Hibi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
Combinatorial Convexity And Algebraic Geometry
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Author :
language : en
Publisher:
Release Date : 1989
Combinatorial Convexity And Algebraic Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Algebraic Geometry Santa Cruz 1995
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Author : János Kollár
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Algebraic Geometry Santa Cruz 1995 written by János Kollár and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Geometry, Algebraic categories.