Günter Ewald

Combinatorial Convexity and Algebraic Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 374
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461240440
• Artikelnr.: 43992831

Autorenporträt

Günter Ewald, geb. 1929, ist emeritierter Professor für Mathematik der Universität Bochum. 1975-1989 war er Mitglied des Präsidiums des Deutschen Evangelischen Kirchentages.

Inhaltsangabe

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.

Rezensionen

"... an excellent addition to the literature of this fascinating research field." J. of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics G. Ewald Combinatorial Convexity and Algebraic Geometry "An excellent addition to the literature of this fascinating research field."-JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS "For anyone wishing to discover the connections between polytopes and algebraic geometry, this readable and well-organized text can be recommended."-MATHEMATICAL REVIEWS

"... an excellent addition to the literature of this fascinating research field." J. of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics

G. Ewald

Combinatorial Convexity and Algebraic Geometry

"An excellent addition to the literature of this fascinating research field."-JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

"For anyone wishing to discover the connections between polytopes and algebraic geometry, this readable and well-organized text can be recommended."-MATHEMATICAL REVIEWS