2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162029This 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.37 pages, 2 figures, submitted for ASPM, Exploration of New Structures and Natural Constructions in Mathematical Physics; ver.2 corrections of some mistakesAlgebraic GeometryHigh Energy Physics - TheoryMathematical Physics14D21; 16G20text