Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009

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Gunnar Fl°ystad, Trygve Johnsen, Andreas Leopold Knutsen
Springer Science & Business Media, May 16, 2011 - Mathematics - 174 pages
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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-S÷derberg 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.

 

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Contents

The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two
1
Koszul Cycles
17
BoijS÷derberg Theory
34
Powers of Componentwise Linear Ideals
49
Modules with 1Dimensional Socle and Components of Lusztig Quiver Varieties in Type A
61
Realization Spaces for Tropical Fans
73
A Relation Between Symmetric Polynomials and the Algebra of Classes Motivated by Equivariant Schubert Calculus
89
Theory and Applications of Lattice Point Methods for Binomial Ideals
99
Geometry and Computation
155
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About the author (2011)

Gunnar Fl°ystad 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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