Abstract
A description is given of those sequences S = ( S ( 0 ) , S ( 1 ) , … , S ( l ) ) \mathbf {S}= (S(0),S(1),\dots ,S(l)) of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors S ( 0 ) , … , S ( l ) S(0),\dots , S(l) . Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series S \mathbf {S} .
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