Arc spaces and the Rogers–Ramanujan identities

  title={Arc spaces and the Rogers–Ramanujan identities},
  author={Clemens Bruschek and Hussein Mourtada and Jan Schepers},
  journal={The Ramanujan Journal},
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. 
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