Polytopes, Rings, and K-Theory | Taschenbuch

Cover: 9781441926173 | Polytopes, Rings, and K-Theory | Winfried Bruns (u. a.) | Taschenbuch

Rückseite: 9781441926173 | Polytopes, Rings, and K-Theory | Winfried Bruns (u. a.) | Taschenbuch

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Beschreibung

This book examines interactions of polyhedral discrete geometry and algebra. What makes this book different from others is the presentation of several central results in all three areas of the exposition - discrete geometry, commutative algebra, and K-theory. The only prerequisite for the reader is a background in algebra, and the basics of polyhedral geometry have been included in Chapter 1.

The text will be of interest to graduate students and mathematicians. Included are numerous exercises, historical background, and notes throughout the chapters.

Über den Autor

Winfried Bruns has contributed numerous articles to homological and combinatorial commutative algebra. The book Cohen-Macaulay Rings he co-wrote with J. Herzog has become a standard reference. His work in discrete convex geometry is presented in the book Polytopes, Rings and K-Theory co-authored with J. Gubeladze, and in the software package Normaliz.

Aldo Conca has written over seventy papers in commutative algebra. His main contributions are related to determinantal rings, Gröbner degenerations, Koszul and quadratic algebras, and Koszul homology. More recently, he has been involved in projects where commutative algebra is applied to "real world" problems.

Claudiu Raicu has contributed to the study of homological invariants in commutative algebra and algebraic geometry, with an emphasis on problems involving symmetries coming from a group action. In the case of determinantal varieties and schemes, his work includes explicit calculations of a number of invariants such as local cohomology groups, Lyubeznik numbers, Hodge ideals, Ext modules and asymptotic regularity.

Matteo Varbaro has contributed to the study of various topics in commutative algebra. His contributions include results on Gröbner deformations, determinantal objects, local cohomology, combinatorial commutative algebra, F-singularities, Castelnuovo-Mumford regularity.

Zusammenfassung

The text will be of interest to graduate students and mathematicians. Included are numerous exercises, historical background, and notes throughout the chapters.

Inhaltsverzeichnis

I Cones, monoids, and triangulations.- Polytopes, cones, and complexes.- Affine monoids and their Hilbert bases.- Multiples of lattice polytopes.- II Affine monoid algebras.- Monoid algebras.- Isomorphisms and automorphisms.- Homological properties and Hilbert functions.- Gr#x00F6;bner bases, triangulations, and Koszul algebras.- III K-theory.- Projective modules over monoid rings.- Bass#x2013;Whitehead groups of monoid rings.- Varieties.

Details

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Monographs in Mathematics
Inhalt:	xiv 461 S. 52 s/w Illustr. 461 p. 52 illus.
ISBN-13:	9781441926173
ISBN-10:	1441926178
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Bruns, Winfried Gubeladze, Joseph
Auflage:	Softcover reprint of hardcover 1st edition 2009
Hersteller:	Springer Springer Monographs in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 26 mm
Von/Mit:	Winfried Bruns (u. a.)
Erscheinungsdatum:	06.12.2010
Gewicht:	0,715 kg