  [Background] A quantitative understanding of neutrino interactions with
nuclei is needed for precision era neutrino long baseline experiments (MINOS,
NOvA, DUNE) which all use nuclear targets. Pion production is the dominant
reaction channel at the energies of these experiments. [Purpose] Investigate
the influence of nuclear effects on neutrino-induced pion production cross
sections and compare predictions for pion-production with available data.
[Method] The Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model is used for
the description of all incohrent channels in neutrino-nucleus reactions.
[Results] Differential cross sections for charged and neutral pion production
for the MINER$\nu$A neutrino and antineutrino flux are calculated. An estimate
for the coherent cross section is obtained from a comparison of data with
theoretical results. The invariant mass ($W$) distribution of the $\Delta$
resonances produced is analyzed. [Conclusions] Final state interactions affect
the pion kinetic energy spectra significantly. The data for charged pion
production at MINER$\nu$A are compatible with the results of calculations using
elementary data taken from an old Argonne National Laboratory experiment.
Remaining differences can be attributed to coherent production; the data for
antineutrino induced neutral pion production, where no coherent contribution is
present, are reproduced quite well. In contrast, the MiniBooNE data, taken at a
lower energy, are consistently higher than the theoretical description. The
analysis of $W$-distributions shows that experimental cuts on this quantity
lead to shape distortions for nuclear targets.
