Essential Dimension and Genericity for Quiver Representations
Federico ScaviaDepartment of Mathematics, University of British Columbia, Vancouver BC V6T 1Z2, Canada
We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We classify the quivers satisfying the genericity property for every dimension vector and show that for every wild quiver the genericity property holds for infinitely many of its Schur roots. We also construct a large class of examples, where the genericity property fails. Our results are particularly detailed in the case of Kronecker quivers.
Cite this article
Federico Scavia, Essential Dimension and Genericity for Quiver Representations. Doc. Math. 25 (2020), pp. 329–364DOI 10.4171/DM/749