arXiv subjects

Ralf Schiffler

Publications and source records attributed to Ralf Schiffler.

74 records · Page 5Linked to original sources

arXiv2004

Quivers with relations arising from clusters (A_n case)

Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type A_n. We associate to each cluster C of U an abelian category Cat_C such that the indecomposable objects of Cat_C are in natural correspondence with the cluster variables of U which are not in C. We give an algebraic realization and a geometric realization of Cat_C. Then, we generalize the ``denominator Theorem'' of Fomin and Zelevinsky to any cluster.

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arXiv2003

Rational smoothness of varieties of representations for quivers of Dynkin type

With the help of Lusztig's canonical basis, we study local intersection cohomology of the Zariski closures of orbits of representations of a quiver of type A, D or E. In particular, we characterize the rationally smooth orbits and prove that orbit closures are smooth if and only if they are rationally smooth. This provides an analogue of theorems of V. Deodhar, and J. Carrell and D. Peterson on Schubert varieties.

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