### Edited 4-Theta embeddings of Jacobians, by Greg W. Anderson

By the Lefschetz embedding theorem,
a principally polarized $g$-dimensional abelian variety is embedded into
projective space by the linear system of
$4^g$ half-characteristic theta functions. Suppose we {\em edit}
this linear system by dropping all the theta functions vanishing at the
origin to order greater than parity requires. We prove that for Jacobians
the edited $4\Theta$ linear system still defines an embedding into
projective space. Moreover, we prove that the
projective models of Jacobians arising from the elementary construction of
Jacobians recently given by the author are (after passage to linear hulls)
copies of the edited
$4\Theta$ model. Thus, for all compact Riemann surfaces, we tie together
algebraic and analytic Jacobians in a new way.

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