  We combine the idea of Chang and Ran [Invent. Math. 76 (1984), 41-54] of
using monads of vector bundles on the projective 3-space to prove the
unirationality of the moduli spaces of curves of low genus with our
classification of globally generated vector bundles with small first Chern
class $c_1$ on the projective 3-space to get an alternative argument for the
unirationality of the moduli spaces of curves of degree at most 13 (based on
the general framework of Chang and Ran).
