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

Cristian Anghel; Iustin Coanda; Nicolae Manolache

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arXiv · 1711.06060

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

Cristian Anghel·Iustin Coanda·Nicolae Manolache

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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).

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Cristian Anghel, Iustin Coanda, Nicolae Manolache. 2017-11-16. On the vector bundles from Chang and Ran's proof of the unirationality of $\mathcal{M}_g$, $g \leq 13$. https://arxiv.org/abs/1711.06060

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