Mathematics – Algebraic Geometry
Scientific paper
1997-01-18
Mathematics
Algebraic Geometry
49 pages, LaTeX
Scientific paper
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.
de Jong Aise Johan
Geemen Bert van
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