Instanton bundles on the blow up of the projective $3$-space at a point

TL;DR

This paper extends the concept of instanton bundles to the blow-up of projective 3-space at a point, providing explicit constructions and analyzing their moduli space properties.

Contribution

It introduces a general definition of instanton bundles on Fano threefolds and constructs explicit examples on the blow-up of -space, linking them to moduli space components.

Findings

Explicit construction of instanton bundles on the blow-up of -space

Identification of smooth points in the moduli space component

Extension of classical instanton definitions to new Fano threefolds

Abstract

We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on $\mathbb P^3$ and on Fano threefold with cyclic Picard group. Then we deal with the case of the blow up of $\mathbb P^3$ at a point, giving an explicit construction of instanton bundles satisfying some important extra properties: moreover, we also show that they correspond to smooth points of a component of the moduli space.