  Let k be an algebraically closed field and let X be a separated scheme of
finite type over k of pure dimension d. We study the structure of the fibres of
the truncation morphisms from the arc space of X to jet spaces of X and also
between jet spaces. Our results are generalizations of results of Denef,
Loeser, Ein and Mustata. We will use them to find the optimal lower bound for
the poles of the motivic zeta function associated to an arbitrary ideal.
