Torsion free instanton sheaves on the blow-up of $\mathbb{P}^{n}$ at a point

TL;DR

This paper introduces a new class of instanton sheaves on the blow-up of projective space, constructing explicit examples and analyzing their moduli, including continuous families in five dimensions.

Contribution

It defines instanton sheaves on the blow-up of projective space, constructs explicit examples, and studies their moduli space, including continuous families in five dimensions.

Findings

Existence of rank 2 instanton sheaves on the blow-up of projective space.

Construction of both locally free and torsion-free examples.

Identification of continuous families filling a smooth component in the moduli space in five dimensions.

Abstract

We define the analogue of instanton sheaves on the blow-up $\widetilde{\mathbb{P}^n}$ of the $n-$dimensional projective space at a point. We choose appropriate polarisation on $\widetilde{\mathbb{P}^n}$ 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 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.