Polytopes, Rings, and K-Theory
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ISBN-13:
9780387763552
Veröffentl:
2009
Erscheinungsdatum:
27.05.2009
Seiten:
461
Autor:
Winfried Bruns
Gewicht:
830 g
Format:
242x164x37 mm
Sprache:
Englisch
Beschreibung:
This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory.
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.
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.
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