We discuss a general framework for the inclusion of heavy quark mass contributions to deep-inelastic structure functions and their perturbative matching to structure functions computed in variable-mass schemes. Our approach is based on the so-called FONLL method, previously introduced and applied to heavy quark hadroproduction and photoproduction. We define our framework, provide expressions up to second order in the strong coupling, and use them to construct matched expressions for structure functions up to NNLO. After checking explicitly the consistency of our results, we perform a study of the phenomenological impact of heavy quark terms, and compare results obtained at various perturbative orders, and with various prescriptions for the treatment of subleading terms, specifically those related to threshold behaviour. We also consider the heavy quark structure function F2c and discuss issues related to the presence of mass singularities in their coefficient functions.

51 pages, 25 figures. Final version, to be published in Nucl. Phys. B. References 19, 20, 24, 36 added; footnote 2 added; comparison to refs.18, 14 added in sect 2.1 and to ref 19 in sect 3.2. Discussion of fig.10 clarified.