Arc Spaces and Rogers-Ramanujan Identities
Algebraic Geometry
2011-02-08 v2 Commutative Algebra
Combinatorics
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-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.
Cite
@article{arxiv.1101.4950,
title = {Arc Spaces and Rogers-Ramanujan Identities},
author = {Clemens Bruschek and Hussein Mourtada and Jan Schepers},
journal= {arXiv preprint arXiv:1101.4950},
year = {2011}
}
Comments
23 pages, introduction rewritten and inaccuracies corrected