  The $1/N_c$-expansion of QCD suggests large flavor asymmetries of the
polarized antiquark distributions in the nucleon. This is confirmed by model
calculations in the large-$N_c$ limit (chiral quark-soliton model), which give
sizable results for $\Delta\bar u (x) - \Delta\bar d (x)$ and $\Delta\bar u (x)
+ \Delta\bar d (x) - 2 \Delta \bar s (x)$. We compute the contributions of
these flavor asymmetries to the spin asymmetries in hadron production in
semi-inclusive deep-inelastic scattering. We show that the large flavor
asymmetries predicted by the chiral quark-soliton model are consistent with the
recent HERMES data for spin asymmetries in charged hadron production.
