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. Les espaces des arcs ont été introduit pour étudier les singularités, mais ils ont aussi un lien fort avec la combinatoire. Ce lien permet une nouvelle approche vers les identités de Rogers-Ramanujan. L'objet permettant cette approche est la série de Hilbert-Poincaré de l'algèbre des arcs centrés en un point de la variété de base. Dans le cas où cette variété est le point double, cette série est la série génératrice des partitions d'un nombre entier sans parties égales ou consécutives.
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