  We establish that the Pauli operator describing a spin-1/2 two-dimensional
quantum system with a singular magnetic field has, under certain conditions, an
infinite-dimensional space of zero modes, possibly, both spin-up and spin-down,
moreover there is a spectral gap separating the zero eigenvalue from the rest
of the spectrum. In particular, infiniteness takes place if the field has
infinite flux, which settles this previously unknown case of Aharonov-Casher
theorem.
