  We study the deeply-virtual Compton scattering (DVCS) process $e^- N \to e^-
\gamma \pi N$ involving the transition between a nucleon and a nucleon
resonance in the $\pi N$ system, within the framework of generalized parton
distributions (GPDs). For the four lowest-lying nucleon resonances,
$\Delta(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, and $S_{11}(1535)$, we express
the DVCS amplitude in the Bjorken limit in terms of corresponding
nucleon-to-resonance GPDs. Building upon the knowledge of the well studied
electromagnetic nucleon-to-resonance transition form factors, which map the
quark charge densities in transverse position space, the corresponding GPDs
will open the prospect to also access the longitudinal momentum distributions
of quarks in the transition. We provide estimates for cross sections and
beam-spin asymmetries in the first and second $\pi N$ resonance regions in the
kinematics of forthcoming CLAS12 data from Jefferson Lab.
