On Weddle surfaces and their moduli
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Michele Bolognesi
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 A2(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 A2(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 ℙ4.
© Walter de Gruyter 2007
Articles in the same Issue
- The ovoidal hyperplanes of a dual polar space of rank 4
- Jørgensen's inequality for metric spaces with application to the octonions
- On multiple blocking sets in Galois planes
- On twisted tensor product group embeddings and the spin representation of symplectic groups
- Projective ovoids and generalized quadrangles
- Multiple farthest points on Alexandrov surfaces
- Stiefel—Whitney classes for coherent real analytic sheaves
- On Weddle surfaces and their moduli
- Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature
Articles in the same Issue
- The ovoidal hyperplanes of a dual polar space of rank 4
- Jørgensen's inequality for metric spaces with application to the octonions
- On multiple blocking sets in Galois planes
- On twisted tensor product group embeddings and the spin representation of symplectic groups
- Projective ovoids and generalized quadrangles
- Multiple farthest points on Alexandrov surfaces
- Stiefel—Whitney classes for coherent real analytic sheaves
- On Weddle surfaces and their moduli
- Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature
