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Arc Spaces and Rogers-Ramanujan Identities

Authors
  • Bruschek, Clemens
  • Mourtada, Hussein
  • Schepers, Jan
Type
Preprint
Publication Date
Feb 07, 2011
Submission Date
Jan 25, 2011
Identifiers
arXiv ID: 1101.4950
Source
arXiv
License
Yellow
External links

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.

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