I consider the single-particle spectral function of the one dimensional Hubbard model below half-filling.
For fixed momentum the spectral function exhibits kinematic thresholds as a function of energy. Above these
thresholds the spectral function exhibits power-law singularities. I determine the threshold exponent, which
is momentum dependent and differs from the Luttinger liquid prediction. The difference arises from irrelevant
perturbations to the low-energy Luttinger liquid description.