We investigate adsorption behaviors and desorption transitions of a fl
exible but self-avoiding polymer on a fluctuating (undulating) membran
e (or interface). Incorporating hard-wall repulsion with polymer-membr
ane attraction of finite range, we find that the membrane fluctuation
gives rise to an effective repulsion and enhances unbinding (desorptio
n) transition of polymer, lowering the transition temperature. Employi
ng hard square-well model as an example, we calculate the desorption t
ransition temperature and the critical behaviors of polymer and membra
ne fluctuations. Our results are qualitatively different from those of
Garel, Kadar and Orland (Europhys. Lett. 29 (1995) 303) who employed
a contact attractive potential which allows the polymer to permeate th
e other side of the surface.