  On plane algebraic curves the so-called Weierstrass kernel plays the same
role of the Cauchy kernel on the complex plane. A straightforward prescription
to construct the Weierstrass kernel is known since one century. How can it be
extended to the case of more general curves obtained from the intersection of
hypersurfaces in a $n$ dimensional complex space? This problem is solved in
this work in the case $n=3$. As an application, the correlation functions of
bosonic string theories are constructed on a canonical curve of genus four.
