Let A be a gentle algebra. It is given by a quiver (directed graph) and 0-relations (non-admissible directed paths). The indecomposable modules of A are determined by the combinatorics of undirected walks on the quiver. So every module admits a diagramme, a family of walks describing it.
We consider the variety of modules of a certain dimension. It admits a group action such that the orbits are the isomorphism classes. We want to consider the union of these orbits based on the underlying diagrammes. We show that they are completely described by the dimensions of certain homomorphism spaces.
Closing the orbits allows us to look at the partial order given by inclusion. This relation is called degeneration. We show that some of them are induced by the so called kissing of string and band diagrammes.