The arc space is the moduli space that parametrizes germs of curves
drawn on a variety X. The space of arcs centered at a point of a scheme
X has a natural cone structure. This permits to define an invariant of
singularities that we call: The Arc Hilbert Poincaré series. In the
first part of the talk, we will describe this invariant and give
motivations for it. We also will show a link between this invariant and
some identities from the theory of integer partitions. In the second
part, we will show how this link to partition theory can be applied to
Groebner bases for some infinitely generated ideals.
The first part is a joint work with Clemens Brucheck and Jan Schepers.
The second part is a work in progress with Pooneh Afsharijoo.