Dependence of Lefschetz maps on the Dolbeault class
= Dependence of Lefschetz maps on the Dolbeault class
{title2=$\phi_{\omega,k}[\alpha]=[\omega^k\wedge\alpha]$}
Wedge multiplication by a closed $(1,1)$ form induces maps on <Dolbeault cohomology>. If $\omega'-\omega=\bar\partial\theta$, then $(\omega')^k-\omega^k=\bar\partial(\theta\wedge\sum_{j=0}^{k-1}(\omega')^j\wedge\omega^{k-1-j})$. Wedging with a closed representative shows that the maps agree. For a change of <Kähler metric potential>, take $\theta=-i\partial f$.