Abstract
The theta function of the Jacobian of a
projective curve induces a solution of an infinite series of
partial differential equations, the KP hierarchy. These
solutions are packaged into the so-called tau function in
integrable systems theory. I will recall the well-known picture
in the case of smooth curves, and I will present some new
results in the case of singular curves, focusing on those curves
for which the theta function is actually polynomial. This is
joint work with T. Çelik and J. Little.