Corollary 23.1.3677FC30E16968

Proof. For a Hermitian form $h$, compactness gives $h\geq c\omega _ n$ for some $c>0$. The potentials $cV_\eta $ satisfy $h+\mathrm{dd}^{\mathrm{c}}(cV_\eta )\geq c(\omega _ n+\mathrm{dd}^{\mathrm{c}}V_\eta )>0$, and positivity of determinants bounds their masses below by $c^ n$ times the divergent masses in theorem 23.1.35. $\square$