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 $M \in \mathrm{Rep}_A^n (k)$ satisfying $\mathrm{Ext}^2_A(M,M)=0$ 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 / Vaccarino, Francesco; Galluzzi, Federica; Ardizzoni, Alessandro. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - STAMPA. - 66:3(2016), pp. 1261-1277.

A new family of algebras whose representation schemes are smooth

VACCARINO, FRANCESCO;
2016

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 $M \in \mathrm{Rep}_A^n (k)$ satisfying $\mathrm{Ext}^2_A(M,M)=0$ are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2641694
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