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

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

2008-08-08

arxiv.org/abs/0808.1318v3

Mathematics

Algebraic Geometry

19 pages. Section 2 replaced by the final one. Further restyling. Same contents

Scientific paper

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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