  For a Riemann surface $X$ and the moduli of regularly stable $G$-bundles $M$,
there is a naturally occuring "$adjoint$" vector bundle over $X \times M$. One
can take the determinant of this vector bundle with respect to the projection
map onto $M$. Our aim here is to study the curvature of the determinant bundle
as the conformal structure on $X$ varies over the Teichm\"uller space.
