A note on the unirationality of a moduli space of double covers

2010/09/22 by Jaya Nn Iyer, Iyer, Jaya NN, Stefan Müller–Stach +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1009.4323

openalex publication_date 2010/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we look at the moduli space \cR_3,2 of double covers of genus three curves, branched along 4 distinct points. This space was studied by Bardelli, Ciliberto and Verra. It admits a dominating morphism \cR_3,2 → \mathcal A₄ to Siegel space. We show that there is a birational model of \cR_3,2 as a group quotient of a product of two Grassmannian varieties. This gives a proof of the unirationality of \cR_3,2 and hence a new proof for the unirationality of \mathcal A₄.

Citations

• The unirationality of the moduli spaces of curves of genus 14 or lower

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