Authors: Clemens Bruschek ¹; Hussein Mourtada ²; Jan Schepers ³

• 1 University of Vienna [Vienna]
• 2 Laboratoire de Mathématiques de Versailles
• 3 Catholic University of Leuven - Katholieke Universiteit Leuven

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-Poincaré 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.