Polymers, which are attached to a membrane at one of their ends, exert an e
ntropic pressure, which curves the membrane away from the polymers. It is s
hown that adsorption which arises from a short-ranged potential between the
polymer and the membrane has a large influence on the curvature of the mem
brane, leading to a decrease of the entropically induced curvature. If one
ignores the finite size of the anchor segment, the polymer-induced curvatur
e does not change sign and vanishes in the limit of strong adsorption and a
pure contact potential. If one includes the finite size of the anchor segm
ent, the membrane beads towards the polymer for sufficiently strung adsorpt
ion.