1997/01/18 by Bert van Geemen, van Geemen, Bert, A. J. de Jong +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.alg-geom/9701007
openalex publication_date 1997/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this connection (which arose in Quantum Field Theory) and characterize it for families of genus two curves. We then consider a particular family (over a configuration space), the corresponding vector bundles are (almost) trivial. The Heat equations which give the connection these bundles are related to the Lie algebra so(6). We compute some local monodromy representations. As a byproduct we obtain, for any representation space V of so(2g+2), a flat connection on the trivial bundle with fiber V over a configuration space and thus a monodromy representation of a pure braid group.