M ar 2 00 6 Codimension two singularities for representations of extended Dynkin quivers
نویسنده
چکیده
Let M and N be two representations of an extended Dynkin quiver such that the orbit O N of N is contained in the orbit closure O M and has codimension two. We show that the pointed variety (O M , N) is smoothly equivalent to a simple surface singularity of type A n , or to the cone over a rational normal curve.
منابع مشابه
N ov 2 00 4 Orbit closures for representations of Dynkin quivers are regular in codimension two
We develop reductions for classifications of singularities of orbit closures in module varieties. Then we show that the orbit closures for representations of Dynkin quivers are regular in codimension two.
متن کاملOn minimal disjoint degenerations of modules over tame path algebras
For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0 → U → M → V → 0 with indecomposable ends that add up to N . We study these ’building blocs’ of...
متن کاملun 2 00 8 Orbifold Singularities , the LATKe , and Pure Yang - Mills with Matter
We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a kind of YangMills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism. E-mail: [email protected] Th...
متن کاملIndecomposable Representations for Extended Dynkin Quivers
We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers Γ over an arbitrary field K by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of indecomposable modules over the corresponding canonical algebra of domestic type. Further, if K is algebraically closed we obtain al...
متن کاملOn minimal disjoint degenerations for preprojective representations of quivers
We derive a root test for degenerations as described in the title. In the case of Dynkin quivers this leads to a conceptual proof of the fact that the codimension of a minimal disjoint degeneration is always one. For Euclidean quivers, it enables us to show a periodic behaviour. This reduces the classification of all these degenerations to a finite problem that we have solved with the aid of a ...
متن کامل