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Monomial Ideals, Computations and Applications

  • Book
  • © 2013

Overview

Editors:
  1. Anna M. Bigatti

    1. Universitá degli Studi di Genova Dipartimento di Matematica, Genova, Italy

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  2. Philippe Gimenez

    1. Geometría y Topología, University of Valladolid, Dpto. de Álgebra, Análisis Matemático, Valladolid, Spain

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  3. Eduardo Sáenz-de-Cabezón

    1. University of La Rioja Matemáticas y Computación, Logroño, Spain

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  • Chapters cover leading-edge aspects of the theory of monomial ideals written by top researchers in their fields
  • Includes computer tutorials that highlight the computational aspects of the area
  • Carefully written introductions to topics of current research interest
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2083)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
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  2. Stanley Decompositions

    1. Front Matter

      Pages 1-1
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    2. A Survey on Stanley Depth

      • Jürgen Herzog
      Pages 3-45

    3. Stanley Decompositions Using CoCoA

      • Anna Maria Bigatti, Emanuela De Negri
      Pages 47-59

  3. Edge Ideals

    1. Front Matter

      Pages 61-61
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    2. A Beginner’s Guide to Edge and Cover Ideals

      • Adam Van Tuyl
      Pages 63-94

    3. Edge Ideals Using Macaulay2

      • Adam Van Tuyl
      Pages 95-105

  4. Local Cohomology

    1. Front Matter

      Pages 107-107
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    2. Local Cohomology Modules Supported on Monomial Ideals

      • Josep Àlvarez Montaner
      Pages 109-178

    3. Local Cohomology Using Macaulay2

      • Josep Àlvarez Montaner, Oscar Fernández-Ramos
      Pages 179-185

  5. Back Matter

    Pages 187-196
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Keywords

About this book

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Editors and Affiliations

  • Universitá degli Studi di Genova Dipartimento di Matematica, Genova, Italy

    Anna M. Bigatti

  • Geometría y Topología, University of Valladolid, Dpto. de Álgebra, Análisis Matemático, Valladolid, Spain

    Philippe Gimenez

  • University of La Rioja Matemáticas y Computación, Logroño, Spain

    Eduardo Sáenz-de-Cabezón

Bibliographic Information

  • Book Title: Monomial Ideals, Computations and Applications

  • Editors: Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-38742-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2013

  • Softcover ISBN: 978-3-642-38741-8Published: 03 September 2013

  • eBook ISBN: 978-3-642-38742-5Published: 24 August 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 194

  • Number of Illustrations: 42 b/w illustrations

  • Topics: Algebra

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