Seshadri slope $\text{K}$-semistability for the blow-up of projective space along a linear subspace

We study a particular instance of the frame work from \cite{Grieve:CM:Line:Slope:Stab}, building on earlier work of Arezzo-et-al \cite{Arezzo:DellaVedova:LaNave}, Ross and Thomas \cite{Ross:Thomas:2007}, \cite{Ross:Thomas:2006} and others, which applies the theory of the Chow-Mumford line bundle to determine the Donaldson-Futaki invariant of deformation to the normal cone test configurations with respect to big and nef line bundles. In particular, here we consider the case of projective $n$-space blown-up along a linear subspace. Our main result arises as an application of \cite[Theorem 1.1]{Grieve:CM:Line:Slope:Stab}. It establishes $\text{K}$-semistability of the deformation to the normal cone test configuration for the blow-up $\text{PP}({\text{Osh}}_{{\text{PP}}^s}^{\oplus r}\oplus {\text{Osh}}_{{\text{PP}}^s}(1))\simeq {\mathrm{Bl}}_{{\text{PP}}^{r-1}}({\text{PP}}^s)$ along the exceptional divisor and with respect to the tautological line bundle ${\text{Osh}}_{\text{PP}({\text{Osh}}_{{\text{PP}}^s}^{\oplus r}\oplus {\text{Osh}}_{{\text{PP}}^s}(1))}(1)$.