  This is the first of two papers studying moduli spaces of a certain class of
coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the
blowup of a projective surface. They are used to relate usual moduli spaces of
stable sheaves on a surface and its blowup. In this first part, we give a
quiver (or ADHM) description of moduli spaces for framed perverse coherent
sheaves on the blowup of the projective plane.
