The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76908We complete the proof of the fact that the moduli space of rank two bundles with trivial determinant embeds into the linear system of divisors on $Pic^{g-1}C$ which are linearly equivalent to $2Θ$. The embedded tangent space at a semi-stable non-stable bundle $ξ\oplusξ^{-1}$, where $ξ$ is a degree zero line bundle, is shown to consist of those divisors in $|2Θ|$ which contain $Sing(Θ_ξ)$ where $Θ_ξ$ is the translate of $Θ$ by $ξ$. We also obtain geometrical results on the structure of this tangent space.33 pages, AMS-LatexAlgebraic Geometry14H60 (Primary), 14H42 (Secondary)The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobiantext