Positivity of coinvariant divisors on M_0,n and the parafermions

2025/06/21 by Chakravarty, Avik
#14H10 #17B69 (primary) #81R10 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2506.17593

Abstract

We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space 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 M_0,n from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles.

Citations

• Conformal Block Divisors for Discrete Series Virasoro VOA Vir_2k+1,2
• Conformal blocks on smoothings via mode transition algebras
• Factorization presentations
• On global generation of vector bundles on the moduli space of curves\n from representations of vertex operator algebras
• Vertex algebras of CohFT-type
• On factorization and vector bundles of conformal blocks from vertex algebras
• Vertex algebras and Teichmüller modular forms
• Parafermion vertex operator algebras and W-algebras
• The irreducible modules and fusion rules for the parafermion vertex operator algebras
• Quantum dimensions and fusion rules for parafermion vertex operator algebras
• Representations of the parafermion vertex operator algebras
• Vanishing and identities of conformal blocks divisors
• Zhu's algebra, C₂-algebra and C₂-cofiniteness of parafermion vertex operator algebras
• Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions
• sl₂ conformal block divisors and the nef cone of M_0,n
• The cone of type A, level one conformal blocks divisors
• Chern classes of conformal blocks
• The structure of parafermion vertex operator algebras: general case
• W-algebras related to parafermion algebras
• Conformal field theories associated to regular chiral vertex operator algebras I: theories over the projective line
• Towards the ample cone of \mgn
• Generalized vertex algebras generated by parafermion-like vertex operators
• The Picard group of the moduli of G-bundles on a curve
• Stable pairs, linear systems and the Verlinde formula

Related

• Line bundles on Contractions of \rmM_0,n via Coinvariant Divisors
• On global generation of vector bundles on the moduli space of curves\n from representations of vertex operator algebras
• Conformal Block Divisors for Discrete Series Virasoro VOA Vir_2k+1,2
• Factorization presentations
• On factorization and vector bundles of conformal blocks from vertex algebras