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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

The Abel Symposium 2009

  • Conference proceedings
  • © 2011

Overview

Editors:
  1. Gunnar Fløystad

    1. Dept. Mathematics, University of Bergen, Bergen, Norway

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  2. Trygve Johnsen

    1. Dept. Mathematics & Statistics, University of Tromsø, Tromsø, Norway

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    You can also search for this editor in PubMed   Google Scholar

  3. Andreas Leopold Knutsen

    1. Dept. Mathematics, University of Bergen, Bergen, Norway

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  • Contains contributions on syzygies, Boij-Söderberg theory, tropical geometry, Schubert calculus, and quiver varieties
  • Contains an introductory survey by E.Miller on binomial ideals and their applications to hypergeometric series, combinatorial games and chemical reactions
  • Contributions by leading researchers on topics in commutative algebra and algebraic geometry related to combinatorics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Abel Symposia (ABEL, volume 6)

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Table of contents (9 papers)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two

    • Mats Boij, Gunnar Fløystad
    Pages 1-16

  3. Koszul Cycles

    • Winfried Bruns, Aldo Conca, Tim Römer
    Pages 17-33

  4. Boij–Söderberg Theory

    • David Eisenbud, Frank-Olaf Schreyer
    Pages 35-48

  5. Powers of Componentwise Linear Ideals

    • Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi
    Pages 49-60

  6. Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A

    • Joel Kamnitzer, Chandrika Sadanand
    Pages 61-72

  7. Realization Spaces for Tropical Fans

    • Eric Katz, Sam Payne
    Pages 73-88

  8. A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus

    • Dan Laksov
    Pages 89-97

  9. Theory and Applications of Lattice Point Methods for Binomial Ideals

    • Ezra Miller
    Pages 99-154

  10. Equations Defining Secant Varieties: Geometry and Computation

    • Jessica Sidman, Peter Vermeire
    Pages 155-174
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Keywords

About this book

The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field.

 

This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Söderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorial games and chemical reactions. 

 

The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour.

Editors and Affiliations

  • Dept. Mathematics, University of Bergen, Bergen, Norway

    Gunnar Fløystad, Andreas Leopold Knutsen

  • Dept. Mathematics & Statistics, University of Tromsø, Tromsø, Norway

    Trygve Johnsen

About the editors

Gunnar Fløystad has published on topics in algebraic geometry, combinatorial commutative algebra and non-commutative algebra.  Trygve Johnsen has published in algebraic geometry and coding theory, and is also interested   in  relations to  matroids. Andreas Leopold Knutsen has published in algebraic geometry, especially in geometry of curves and surfaces, and in birational geometry.

Bibliographic Information

  • Book Title: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

  • Book Subtitle: The Abel Symposium 2009

  • Editors: Gunnar Fløystad, Trygve Johnsen, Andreas Leopold Knutsen

  • Series Title: Abel Symposia

  • DOI: https://doi.org/10.1007/978-3-642-19492-4

  • Publisher: Springer Berlin, Heidelberg

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

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Hardcover ISBN: 978-3-642-19491-7Published: 18 May 2011

  • Softcover ISBN: 978-3-642-26828-1Published: 15 July 2013

  • eBook ISBN: 978-3-642-19492-4Published: 16 May 2011

  • Series ISSN: 2193-2808

  • Series E-ISSN: 2197-8549

  • Edition Number: 1

  • Number of Pages: XIV, 174

  • Topics: Commutative Rings and Algebras, Algebraic Geometry, Combinatorics

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