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

الأصل · EN

We 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 Picᵍ⁻¹C which are linearly equivalent to 2Θ. The embedded tangent space at a semi-stable non-stable bundle ξ⊕ξ⁻¹, where ξ is a degree zero line bundle, is shown to consist of those divisors in |2Θ| which contain Sing(Θξ) where Θξ is the translate of Θ by ξ. We also obtain geometrical results on the structure of this tangent space.