  The thermal and fragmentation properties of star-forming clouds have
important consequences on the corresponding characteristic stellar mass. The
initial composition of the gas within these clouds is a record of the
nucleosynthetic products of previous stellar generations. In this paper we
present a model for the evolution of star-forming clouds enriched by metals and
dust from the first supernovae, resulting from the explosions of metal-free
progenitors with masses in the range 12 - 30 Msun and 140 - 260 Msun. Using a
self-consistent approach, we show that: (i) metals depleted onto dust grains
play a fundamental role, enabling fragmentation to solar or sub-solar mass
scales already at metallicities Zcr = 10^{-6} Zsun; (ii) even at metallicities
as high as 10^{-2} Zsun, metals diffused in the gas-phase lead to fragment mass
scales which are ~ 100 Msun; (iii) C atoms are strongly depleted onto amorphous
carbon grains and CO molecules so that CII plays a minor role in gas cooling,
leaving OI as the main gas-phase cooling agent in low-metallicity clouds. These
conclusions hold independently of the assumed supernova progenitors and suggest
that the onset of low-mass star formation is conditioned to the presence of
dust in the parent clouds.
