On Weddle surfaces and their moduli

Abstract

Abstract The Weddle surface is classically known to be a birational (partially desingularized) model of the Kummer surface. In this note we go through its relations with moduli spaces of abelian varieties and of rank two vector bundles on a genus 2 curve. First we construct a moduli space A 2 (3) − parametrizing abelian surfaces with a symmetric theta structure and an odd theta characteristic. Such objects can in fact be seen as Weddle surfaces. We prove that A 2 (3) − is rational. Then, given a genus 2 curve C , we give an interpretation of the Weddle surface as a moduli space of extensions classes (invariant with respect to the hyperelliptic involution) of the canonical sheaf ω of C with ω −1 . This in turn allows to see the Weddle surface as a hyperplane section of the secant variety Sec( C ) of the curve C tricanonically embedded in ℙ 4 .

Locations

• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
• Advances in Geometry - View