# Jan Christophersen (UiO): Derivations of artinian algebras and rigidity of curve singularities

**Abstract: **Let A be a local artinian algebra over an algebraically closed field k of characteristic 0. There is a conjecture that the vector space dimension of the derivations of A is greater or equal the vector space dimension of the maximal ideal of A. Moreover equality should only happen when A is a hypersurface. We will show that this conjecture would imply non-rigidity of reduced curve singularities and describe various attempts to prove the conjecture. In particular we relate the problem to the GL(n) representation on n commuting n x n matrices.Derivations of artinian algebras and rigidity of curve singularities

Published Nov. 21, 2016 1:20 PM
- Last modified July 31, 2018 12:27 PM