Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions

Avik Chakravarty

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arXiv · 2506.17593

Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions

Avik Chakravarty

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Abstract

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.

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BibTeX RIS

Avik Chakravarty. 2025-06-21. Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions. https://arxiv.org/abs/2506.17593

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