The present disclosure is directed, in part, to a curable composition, a method for augmenting a structure in a patient with a resorbable biocompatible polymer, and a biodegradable, resorbable implant comprising a biocompatible copolymer. An exemplary embodiment of the curable composition comprises (a) 60 wt. % to 95 wt. % of one or more vinyl ester monomers and/or vinylcarbonate monomers, wherein said one or more vinyl ester monomers and/or vinylcarbonate monomers are respectively selected from compounds of the general formulas (I) and (II) below: wherein n, m R1 and R2 have the meaning defined herein; (b) 0.1 to 40 wt. % of one or more multifunctional thiols; and (c) 0 to 10 wt. % of a biocompatible polymerization initiator.