Resumen:
The cone structure of the space of arcs centered at a point
of a scheme X, permits to define a new invariant of singularities that we
call: The Arc Hilbert Poincaré series. We will describe this invariant
and compute it in some simple cases (smooth varieties, rational double point
singularities, normal crossing divisors). When X is the double point
Spec(k[y]/y2), the result is surprising: our series is the series that
appears in the first identity of the Rogers-Ramanujan Identities.
This is joint work with Clemens Bruschek an Jan Schepers.
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