41 research outputs found
Jet schemes of complex plane branches and equisingularity
For , we determine the irreducible components of the -th
Jet Scheme of a complex branch and give formulas for their number
and for their codimensions, in terms of and the generators of the semigroup
of . This structure of the Jet Schemes determines and is determined by the
topological type of .Comment: 22 page
Neighborly partitions, hypergraphs and Gordon's identities
We prove a family of partition identities which is "dual" to the family of
Andrews-Gordon's identities. These identities are inspired by a correspondence
between a special type of partitions and "hypergraphs" and their proof uses
combinatorial commutative algebra
Arc Spaces and Rogers-Ramanujan Identities
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.Comment: 23 pages, introduction rewritten and inaccuracies correcte