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

On the vector bundles from Chang and Ran's proof of the unirationality of $\mathcal{M}_g$, $g \leq 13$