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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.

April 25, 2026

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.

Abstract

Abstract We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space M₀, ₍ 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 M₀, ₍ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles.

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Authors

Avik Chakravarty

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International Mathematics Research Notices

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University of Pennsylvania

Philadelphia University

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

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Abstract

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