Description

Book Synopsis
Deals with the interplay of computational commutative algebra and the theory of convex polytopes. This title centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties.

Table of Contents
Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The second hypersimplex $\mathcal A$-graded algebras Canonical subalgebra bases Generators, Betti numbers and localizations Toric varieties in algebraic geometry Some specific Grobner bases Bibliography Index.

Grobner Bases and Convex Polytopes

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A Paperback by Bernd Sturmfels

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    View other formats and editions of Grobner Bases and Convex Polytopes by Bernd Sturmfels

    Publisher: MP-AMM American Mathematical
    Publication Date: 12/30/1995 12:00:00 AM
    ISBN13: 9780821804872, 978-0821804872
    ISBN10: 0821804871
    Also in:
    Combinatorics and graph theory Discrete mathematics

    Description

    Book Synopsis
    Deals with the interplay of computational commutative algebra and the theory of convex polytopes. This title centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties.

    Table of Contents
    Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The second hypersimplex $\mathcal A$-graded algebras Canonical subalgebra bases Generators, Betti numbers and localizations Toric varieties in algebraic geometry Some specific Grobner bases Bibliography Index.

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