  We study the production of heavy quarks in deep-inelastic scattering within
perturbative QCD. As a novelty, we employ for the first time the running mass
definition in the MSbar scheme for deep-inelastic charm and bottom production.
We observe an improved stability of the perturbative expansion and a reduced
theoretical uncertainty due to variations of the renormalization and
factorization scales. As our best estimate we extract from a global fit to
fixed-target and HERA collider data for the charm-quark an MSbar mass of
m_c(m_c) = 1.01 +- 0.09 (exp) +- 0.03 (th) GeV.
