### An explicit algebraic representation of the Abel map, by Greg W. Anderson

This paper has appeared in International Math Research Notices 1997, No.
11, 495-521, and so the dvi version has been removed.
Given a nonsingular projective curve (defined over an
algebraically closed field of any characteristic) of genus $g$
and an effective divisor $G$ on that curve of positive even degree not less
than $4g$, we write down a reasonably simple and explicit system
of equations and inequalities the solutions of which we prove to be
canonically in bijective correspondence with the divisor classes of
degree equal to $\frac{1}{2}\deg G$. The paper is set at a very
elementary level. Our results are formulated and proved
in the context of the theory of algebraic functions of one variable.
We make no use of sophisticated cohomological tools;
instead we rely upon a $19^{th}$-century-style construction
that we call the {\em abeliant}.

Greg W. Anderson <gwanders@math.umn.edu>