Let $X$ be a Nodal curve. Let $\bar{J}(X)$ be compactified Jacobian (rank one torsion free sheaf of degree one) and $\Theta$ denote the theta divisor in $J$. How to compute $H^0(\bar{J}(X);\Theta^k)$, or $h^0(\bar{J}(X);\Theta^k)$? What is known about these groups?
