  The irreducible components of varieties parametrizing the finite dimensional
representations of a finite dimensional algebra $\Lambda$ are explored, with
regard to both their geometry and the structure of the modules they encode.
Provided that the base field is algebraically closed and has infinite
transcendence degree over its prime field, we establish the existence and
uniqueness (not up to isomorphism, but in a strong sense to be specified) of a
generic module for any irreducible component $\mathcal C$, that is, of a module
which displays all categorically defined generic properties of the modules
parametrized by $\mathcal C$; the crucial point of the existence statement - a
priori almost obvious - lies in the description of such a module in a format
accessible to representation-theoretic techniques. Our approach to generic
modules over path algebras modulo relations, by way of minimal projective
resolutions, is largely constructive. It is explicit for large classes of
algebras of wild type. We follow with an investigation of the properties of
such generic modules in terms of quiver and relations. The sharpest specific
results on all fronts are obtained for truncated path algebras, that is, for
path algebras of quivers modulo ideals generated by all paths of a fixed
length; this class of algebras extends the comparatively thoroughly studied
hereditary case, displaying many novel features.
