Construction of Hodge structures on the SO(3) modular functors

2024/02/26 by Godfard, Pierre
#14D07 #20G42 (Primary) 14H10 #32G15 (Secondary) #57R56 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2402.16804

Abstract

We prove that SO(3) modular functors in genus 0 have geometric origin and support integral variations of Hodge structures for any odd level r and r-th root of unity ζ_r∈ℂ. We identify the TQFT intersection forms and integral structures with the geometric ones. Moreover, the gluing property of the modular functors is recovered geometrically as a Künneth formula. The construction is based on the homological models of Felder-Wieczerkowski and Martel.

Related

• Hodge structures on conformal blocks
• Modular forms on GL(3) and Galois representations
• Tame topology of arithmetic quotients and algebraicity of Hodge loci
• The E³/Z3 orbifold, mirror symmetry, and Hodge structures of Calabi-Yau type
• The Hodge-de~Rham Theory of Modular Groups