## Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009Gunnar Fløystad, Trygve Johnsen, Andreas Leopold Knutsen 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. |

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### Contents

The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two | 1 |

Koszul Cycles | 17 |

BoijSöderberg 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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### Common terms and phrases

A-graded affine semigroup ring artinian artinian modules associated prime Betti diagram Betti tables binomial ideal binomial primary decomposition blowup chordal graph codimension Cohen–Macaulay coherent sheaves cohomology tables combinatorial game Commutative Algebra complex componentwise linear compute cone Conjecture connected component coordinate Corollary corresponding d-dimensional d-sequence with respect defined Definition denote dimension divisor Eisenbud elements equivariant Example extremal rays Fløystad follows free resolution graph heap Hence Hilbert function homogeneous homomorphism hyperplane integer intersection isomorphism Koszul lattice game lattice points Lemma line bundle linear resolution Math matroid matroid fan mesoprimary minimal mis`ere quotients module monoid monomial morphism multigraded multiplicity nonzero order ideal polynomial ring primary decomposition Proof Proposition rational normal curve regs(I Schur polynomials secant variety Sect semigroup ring sequence subset subvariety surjective syzygies Theorem theory total degrees tropical realization space variables vector bundles vector space vertex cover zero