We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space $\overline{ \mathrm{ M}}_{ 0,n}$ of rational curves with $n$ marked points. The criteria use the multiplicative structure of VOA representations encoded in the fusion ring. Using them, we construct positive line bundles on $\overline{ \mathrm{ M}}_{ 0,n}$ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles.
Categories: math.AG math.QA