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MSRI Streaming Video Series <BR> Christine Riedtmann
- Degenerations of modules
<BR> 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. <p>
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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.
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