2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107497The 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 ωof 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^4.35 pages, to appear in Advances in Geometry, part of the author's Phd ThesisAlgebraic Geometry14K10, 14E05, 14H60text