Torsion free instanton sheaves on the blow-up of [formula omitted] at a point

Abstract

We define the analogue of instanton sheaves on the blow-up Pn˜ of the n-dimensional projective space at a point. We choose an appropriate polarisation on Pn˜ and construct rank 2 examples of locally free and non locally free (but torsion free) type. In general, the defined instantons also turn out to be the cohomology of monads, although non-linear ones. Moreover, in the five dimensional case, we show that there are continuous families of them that fill, at least, a smooth component in the moduli of semi-stable sheaves.