Understanding finite dimensional representations generically

摘要: We survey the development and status quo of a subject best described as “generic representation theory finite dimensional algebras”, which started taking shape in early 1980s. Let \({\Lambda }\) be algebra over an algebraically closed field. Roughly, aims at (a) pinning down irreducible components standard parametrizing varieties for }\)-modules with fixed dimension vector, (b) assembling generic information on modules each individual component, that is, data shared by all dense open subset component. present overview results spanning spectrum from hereditary algebras through tame non-hereditary case to wild algebras.