The rationality of the moduli space of genus four curves endowed with an order three subgroup of their Jacobian

Ingrid Bauer; Alessandro Verra

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arXiv · 0808.1318

The rationality of the moduli space of genus four curves endowed with an order three subgroup of their Jacobian

Ingrid Bauer·Alessandro Verra

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Abstract

Refereed version to appear in Michigan Mathematical Journal. A mistake in the last section of the previous version has been corrected. The new title exactly describes the main result obtained. Building on the geometry of cubic surfaces and on a theorem of Dolgachev, the rationality of the moduli space R mentioned in the title is proved. Let M be the moduli space of 6 points in the plane, modulo the natural involution induced by double-six configurations on cubic surfaces. It is proved that R is birational to a tower of locally trivial projective bundles ending onto M. The rationality of R then follows from Dolgachev's theorem that M is rational.

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BibTeX RIS

Ingrid Bauer, Alessandro Verra. 2009-05-16. The rationality of the moduli space of genus four curves endowed with an order three subgroup of their Jacobian. https://arxiv.org/abs/0808.1318

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