Monads for torsion-free sheaves on multi-blow-ups of the projective plane

Abstract

We construct monads for framed torsion-free sheaves with fixed Chern character on the multi-blow-ups of the complex projective plane. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we construct monads for families of such sheaves parametrized by a reduced noetherian scheme $S$ of finite type. A universal monad on the moduli space is introduced and used to prove that the moduli space is fine.