Notes of the inversion of integrals. I

Abstract:

If $W$ is a Picard bundle on the Jacobian $J$ of a curve $C$, we have the problem of describing $W$ globally. The theta divisor $\theta$ is ample on $J$. Thus it is possible to write ${n^ * }W$ as the sheaf associated to a graded $M$ over the well-known ring ${ \oplus _{m \geq 0}}\Gamma (J,{\mathcal {O}_J}(m4\theta ))$. In this paper we compute the degree of generators and relations for such a module $M$.