Arc spaces have been introduced in algebraic geometry as a tool to study
singularities but they show strong connections with combinatorics as well.
Exploiting these relations we obtain a new approach to the classical
Rogers-Ramanujan Identities. The linking object is the Hilbert-Poincar\'e
series of the arc space over a point of the base variety. In the case of the
double point this is precisely the generating series for the integer partitions
without equal or consecutive parts.Comment: 23 pages, introduction rewritten and inaccuracies correcte
