  In this paper we use A-infinity modules to study the derived category of a
finite dimensional algebra over an algebraically closed field. We study
varieties parameterising A-infinity modules. These varieties carry an action of
an algebraic group such that orbits correspond to quasi-isomorphism classes of
complexes in the derived category. We describe orbit closures in these
varieties, generalising a result of Zwara and Riedtmann for modules.
