This note examines the geometry behind the Hamiltonian structure of
isomonodromy deformations of connections on vector bundles over Riemann
surfaces. The main point is that one should think of an open set of the moduli
of pairs (V,β) of vector bundles and connections as being obtained by
"twists" supported over points of a fixed vector bundle V0β with a fixed
connection β0β; this gives two deformations, one, isomonodromic, of
(V,β), and another induced from the isomonodromic deformation of
(V0β,β0β). The difference between the two will be Hamiltonian.Comment: 20 page