Generalized Weierstrass Kernels on the Intersection of Two Complex Hypersurfaces

Details Generalized Weierstrass Kernels on the Intersection of Two Complex Hypersurfaces Generalized Weierstrass Kernels on the Intersection of Two Complex Hypersurfaces

2000-12-14

arxiv.org/abs/math/0012109v2

Mathematics

Algebraic Geometry

plain TeX, 44 pages, no figures, corrected some misprints in the bibliography

Scientific paper

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.

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