Abstract
The Jacobian
J
of a complete, smooth, connected curve
X
admits a canonical divisor
Θ
, called the Theta divisor. It is well-known that
Θ
is ample and, in fact,
3Θ
is very ample. For a general complete, integral curve
X
, D'Souza constructed a compactification
J
¯
of the Jacobian
J
by considering torsion-free, rank 1 sheaves on
X
. Soucaris and the author considered independently the analogous Theta divisor
Θ
on
J
¯
, and showed that
Θ
is ample. In this article, we show that
nΘ
is very ample for
n
greater or equal to a specified lower bound. If
X
has at most ordinary nodes or cusps as singularities, then our lower bound is 3. Our main tool is to use theta sections associated to vector bundles on
X
to embed
J
¯
into a projective space.