2008/08/08 by Ingrid Bauer, Alessandro Verra, Bauer, Ingrid +1
Arts and Humanities · Mathematics · #14H10 #14H45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #math.AG #msc:14H10 #msc:14H45
paper · pdf · doi:10.48550/arxiv.0808.1318
19 pages. Section 2 replaced by the final one. Further restyling. Same contents
openalex publication_date 2008/08/08 · arxiv created 2009/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.