On the smoothness of the scheme of linear representations and the Nori-Hilbert scheme of an associative algebra

Abstract

Let $k$ be an algebraically closed field and let $A$ be a finitely generated $k-$algebra. We show that the scheme of n-dimensional representations of $A$ is smooth when $A$ is hereditary and coherent. We deduce from this the smoothness of the Nori-Hilbert scheme associated to $A.$

arXiv comment20 pages, submitted for publication

References in corpus (2)

• Cohomology of non-commutative Hilbert schemes
• Moduli of linear representations, symmetric products and the non commutative Hilbert scheme