Arc Spaces and Rogers-Ramanujan Identities

Abstract

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.

Keywords

• formal power series
• hilbert-poincaré series
• partitions
• rogers-ramanujan identities
• arc spaces
• infinite dimensional gröbner basis
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]