We calculate and analyze the O(alpha(s)) one-particle inclusive cross
section in polarized deep inelastic lepton-hadron scattering, using di
mensional regularization and the HVBM prescription for ys We discuss t
he factorization of all the collinear singularities related to the pro
cess, particularly those that are absorbed in the redefinition of the
spin-dependent analogue of the recently introduced fracture functions,
This is done in the usual <(MS)over bar> scheme and in another one, c
alled <(MS(p))over bar>, which factorizes soft contributions and guara
ntees the axial current (non-)conservation properties.