  The properties of net quark number fluctuations in the vicinity of the QCD
chiral phase transition are discussed in terms of an effective chiral model in
the mean-field approximation. We focus on the ratio of the fourth- to second-
order cumulants (kurtosis) and the compressibility of the system and discuss
their dependence on the pion mass. It is shown that near the chiral phase
transition, both observables are sensitive to the value of $m_\pi$. For
physical $m_\pi$, the kurtosis exhibits a peak whereas the inverse
compressibility shows a dip at the pseudocritical temperature. These structures
disappear for large $m_\pi$. Our results, obtained in an effective model with
two flavors, are qualitatively consistent with recent results of 2+1 flavor
lattice gauge theory. We also discuss the high- and low-temperature properties
of these observables and the role of the coupling of the quark degrees of
freedom to the Polyakov loop.
