%0 Journal Article %T Perverse coherent sheaves on blow-up. I. a quiver description %A Hiraku Nakajima %A Kota Yoshioka %J Mathematics %D 2008 %I arXiv %X 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. %U http://arxiv.org/abs/0802.3120v2