Poincare series of line bundles on varieties

We associate a Poincare series to the dimension of global sections of multiples of r line bundles on a proper variety X. We show that this series is rational on a nonsingular characteristic 0 curve, but can be irrational on a singular curve, and can be irrational in higher dimensions. We also show that the series can be irrational in positive characteristic, even on a nonsingular curve.