Arc Spaces and Rogers-Ramanujan Identities

Details Arc Spaces and Rogers-Ramanujan Identities Arc Spaces and Rogers-Ramanujan Identities

2011-01-25

arxiv.org/abs/1101.4950v2

Mathematics

Algebraic Geometry

23 pages, introduction rewritten and inaccuracies corrected

Scientific paper

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.

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