  The one-particle inclusive cross section in deeply inelastic lepton--nucleon
scattering, expressed in terms of parton densities and fragmentation functions
being differential in the invariant mass of the observed hadron and of the
incoming nucleon, diverges if this invariant mass vanishes. This divergence can
be traced back to the kinematical configuration where the parent parton of the
observed hadron is emitted collinearly from the incoming parton of the QCD
subprocess. By using the concept of ``fracture functions'', which has recently
been introduced by Trentadue and Veneziano, it is possible to absorb this
divergence in these new distribution functions as long as the observed hadron
is not soft. This procedure allows the determination of a finite one-particle
inclusive cross section in next-to-leading order QCD perturbation theory. We
give details of the calculation and the explicit form of the bare fracture
functions in terms of the renormalized ones.
