Hodge structures on conformal blocks

2024/06/11 by Godfard, Pierre
#14D07 #14H10 (primary) 57R56 #18M20 #20G42 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2406.07459

Abstract

We prove existence and uniqueness of complex Hodge structures on modular functors. The proof is based on the non-Abelian Hodge correspondence and Ocneanu rigidity. Given a modular functor, we explain how its Hodge numbers fit into a Frobenius algebra and the Chern characters of its Hodge decompositions into a new cohomological field theory (CohFT). In the case of SU(2) modular functors of level 2 times an odd number, we give explicit formulas for all Hodge numbers, in any genus g.

Related

• Construction of Hodge structures on the SO(3) modular functors
• Geometric Hodge structures with prescribed Hodge numbers
• Hodge structures Orbifold hodge numbers and a correspondence in Quasitoric Orbifolds
• Hodge structures not coming from geometry
• XI Solomon Lefschetz Memorial Lecture Series: Hodge structures in non-commutative geometry. (Notes by Ernesto Lupercio)