6533b7d0fe1ef96bd125ba22
RESEARCH PRODUCT
A note on the unirationality of a moduli space of double covers
Stefan Müller-stachJaya Nn Iyersubject
Pure mathematicsModular equationGeneral MathematicsModuli spaceModuli of algebraic curvesAlgebraMathematics - Algebraic GeometryMathematics::Algebraic GeometryMorphismGenus (mathematics)GrassmannianFOS: MathematicsGeometric invariant theoryAlgebraic Geometry (math.AG)QuotientMathematicsdescription
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 $\cR_{3,2} \to {\mathcal A}_4$ 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 ${\mathcal A}_4$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-09-22 | Mathematische Nachrichten |