Solutions of the KZB equations in genus ≥ 1

1999/12/24 by Benjamin Enriquez, B. Enriquez, Enriquez, B. +3
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/9912198

openalex publication_date 1999/12/24 · arxiv created 2000/01/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a flat version of the KZB connection. This connection is defined on the complement of the locus of Weierstrass points on the moduli space of genus g complex curves with marked points. We then give integral formulas for flat sections of this connection, using the parametrization of conformal blocks and of the KZB connection of our earlier paper math/9807145.

Citations

• Commuting differential and difference operators associated to complex curves, I
• Invariants of 3-manifolds via link polynomials and quantum groups
• Classical and quantum conformal field theory
• Factorizable sheaves and quantum groups

Related

• The KZB equations on Riemann surfaces
• Universal KZB Equations for arbitrary root systems
• Conformal blocks in genus zero and the KZ connection
• On p-adic solutions to KZ equations, ordinary crystals, and p^s-hypergeometric solutions
• Geometrization of the TUY/WZW/KZ connection