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

Abstract

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).

v4: the alternative constructions have been removed for brevity

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• Globally Generated Vector Bundles on P^n with c_1=4
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Cited by in corpus (1)

• Globally generated vector bundles with $c_1=5$ on ${\mathbb{P}}^n$, $n\ge 4$