Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

1. Front Matter

   Pages I-XIV

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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

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.

• algebraic geometry
• combinatorics
• commutative algebra

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

  Gunnar Fløystad, Andreas Leopold Knutsen

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

  Trygve Johnsen

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.

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