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1.
It is known that the orbit closures for the representations of the equioriented Dynkin quivers ?
n
are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers
?
n
with arbitrary orientation.
Received: 25 October 2000 / Revised version: 28 February 2001 相似文献
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We show that the set of common zeros of all semi-invariants vanishing at 0 on the variety of all representations with dimension vector of an extended Dynkin quiver under the group is a complete intersection if is ``big enough'. In case does not contain an open -orbit, which is the case not considered so far, the number of irreducible components of grows with , except if is an oriented cycle.
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5.
Singularities of Orbit Closures in Module Varieties and Cones Over Rational Normal Curves 总被引:1,自引:0,他引:1
Let N be a point of an orbit closure Min a module variety such that its orbit N has codimension 2in M. We show that under someadditional conditions the pointed variety (M, N) is smoothly equivalent to a cone over a rationalnormal curve. 相似文献
6.
Grzegorz Zwara 《manuscripta mathematica》2007,123(3):237-249
Let M and N be two representations of an extended Dynkin quiver such that the orbit of N is contained in the orbit closure and has codimension two. We show that the pointed variety is smoothly equivalent to a simple surface singularity of type A
n
, or to the cone over a rational normal curve. 相似文献
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We study degeneration-like orders on the additive categories of pairwise orthogonal generalized standard components of the Auslander-Reiten quivers of artin algebras. 相似文献
9.
Christine?RiedtmannEmail author Grzegorz?Zwara 《Commentarii Mathematici Helvetici》2004,79(2):350-361
Let d be a prehomogeneous
dimension vector for a finite
tame quiver Q.
We show that the common zeros of all
non-constant semi-invariants for the variety of representations
of Q with dimension vector
$N\cdot\mathbf d$, under the product of the general linear groups at all vertices,
is a complete intersection for $N\geq 3$. 相似文献
10.
We prove that the derived equivalences (more generally the stable equivalences of Morita type) of finite dimensional selfinjective algebras over algebraically closed fields preserve the types of singularities in the orbit closures of module varieties. As an application, we obtain that the orbit closures in the module varieties of the Brauer tree algebras are normal and Cohen-Macaulay.
Mathematics Subject Classification (2000):14B05, 14L30, 16D50, 16G20 相似文献