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

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

1998-05-07

arxiv.org/abs/math/9805037v1

Mathematics

Algebraic Geometry

33 pages, AMS-Latex

Scientific paper

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 $Pic^{g-1}C$ which are linearly equivalent to $2\Theta$. The embedded tangent space at a semi-stable non-stable bundle $\xi\oplus\xi^{-1}$, where $\xi$ is a degree zero line bundle, is shown to consist of those divisors in $|2\Theta|$ which contain $Sing(\Theta_{\xi})$ where $\Theta_{\xi}$ is the translate of $\Theta$ by $\xi$. We also obtain geometrical results on the structure of this tangent space.

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