Steiner representations of hypersurfaces

Let [Formula: see text] be an integral hypersurface of degree [Formula: see text]. We show that each locally Cohen–Macaulay instanton sheaf [Formula: see text] on [Formula: see text] with respect to [Formula: see text] in the sense of [V. Antonelli and G. Casnati, Instanton sheaves on projective schemes, J. Pure Appl. Algebra 227 (2023) 107246, Definition 1.3] yields the existence of Steiner bundles [Formula: see text] and [Formula: see text] on [Formula: see text] of the same rank [Formula: see text] and a morphism [Formula: see text] such that the form defining [Formula: see text] to the power [Formula: see text] is exactly [Formula: see text]. We inspect several examples for low values of [Formula: see text], [Formula: see text] and [Formula: see text]. In particular, we show that the form defining a smooth integral surface in [Formula: see text] is the pfaffian of some skew-symmetric morphism [Formula: see text], where [Formula: see text] is a suitable Steiner bundle on [Formula: see text] of sufficiently large even rank.