We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field. In particular, our result implies that the points $M in an (k)$ satisfying $Ext _A ^2(M,M)=0$ are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.
A new family of algebras whose representation schemes are smooth
ARDIZZONI, Alessandro;GALLUZZI, Federica;
2016-01-01
Abstract
We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field. In particular, our result implies that the points $M in an (k)$ satisfying $Ext _A ^2(M,M)=0$ are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.
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