  We prove the Polyakov conjecture on the supertorus $(ST_2)$: we dermine an
iterative solution at any order of the superconformal Ward identity and we show
that this solution is resumed by the Wess-Zumino-Polyakov (WZP) action that
describes the $(1,0)$ 2D-supergravity. The resolution of the superBeltrami
equation for the Wess-Zumino (WZ) field is done by using on the one hand the
Cauchy kernel defined on $ST_2$ and on the other hand, the formalism developed
to get the general solution on the supercomplex plane. Hence, we determine the
n-points Green functions from the (WZP) action expressed in terms of the (WZ)
field.
