Degenerations of modules

Christine Riedtmann

Abstract: If \Lambda is a finite dimensional associative algebra over an algebraically closed field k, the \Lambda-module structures on k^d can be regarded as an affine variety over k: just specify the matrices corresponding to generators of \Lambda and the relations that these generators - and hence the matrices - must satisfy. A module N is called a degeneration of M if N belongs to the Zariski closure of the isomorphism class of M in this variety.

I want to give examples of degenerations, explain some background and finally show Zwara's theorem: N is a degeneration of M if and only if there is a short exact sequence of \Lambda-modules 0 \to S \to S\oplus M \to N \to 0 for some S.

created Mon Mar 20 12:39:20 PST 2000