Titlebook: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry; The Abel Symposium 2 Gunnar Fløystad,Trygve Johnsen,Andreas Leopold Kn

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The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two,pe when taking total degrees. If the differences, . and ., of these total degrees are relatively prime, the extremal rays are parametrized by order ideals in ℕ. contained in the region .+.<(.−1)(.−1). We also consider some examples concerning artinian modules of codimension three.

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Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A,We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they may be used to describe the components of Lusztig quiver varieties.

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The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two,pe when taking total degrees. If the differences, . and ., of these total degrees are relatively prime, the extremal rays are parametrized by order ideals in ℕ. contained in the region .+.<(.−1)(.−1). We also consider some examples concerning artinian modules of codimension three.

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