  To explain the low frequencies of quantum oscillations observed in lightly
doped cuprates, we consider the two-dimension Hubbard model supplemented with
the perpendicular magnetic field. For large Hubbard repulsions, the electron
spectrum is investigated using the cluster perturbation theory. Obtained
frequencies of magnetic oscillations at small deviations from half-filling are
close to those observed experimentally, $F\approx500$~T. They stem from small
Fermi surface pockets located in the nodal regions of the Brillouin zone. The
pockets are formed by Fermi arcs and less intensive segments, which make the
pockets nearly circular.
