Vanishing theorems on (ℓ|k)(ℓ|k)-strong Kähler manifolds with torsion

We derive sufficient conditions for the vanishing of plurigenera, pm(J),m>0pm(J),m>0, on compact (ℓ|k)(ℓ|k)-strong, ωℓ∧∂∂̄ωk=0, Kähler manifolds with torsion. In particular, we show that the plurigenera of closed (ℓ|k)(ℓ|k)-strong manifolds, k