Positivity of Coinvariant Divisors on M 0, n and the Parafermions

Key Points

• This research focuses on the criteria for establishing the positivity of line bundles derived from vertex operator algebras on the moduli space of rational curves.
• Criteria for positivity are derived from the fusion ring of VOAs.
• Construct positive line bundles on the moduli space using parafermion VOAs.
• First examples of commutant VOAs producing positive line bundles are presented.
• Positive line bundles are successfully constructed on the moduli space from parafermion VOAs.
• The criteria rely on the multiplicative structure of the respective VOA representations.