\end{align}Recall that there is the isomorphism\textbf{RHom}(\mathbf{L}_{X_0/\text{Spec}(k)},\mathcal{O}_{X_0}[+1]) \cong \text{Ext}^1(\mathbf{L}_{X_0/\text{Spec}(k)}, \mathcal{O}_{X_0})from general theory of derived categories, and the ext group classifies the first-order deformations. Then, through a series of reductions, this group can be computed. First, since \mathbf{L}_{\mathbb{A}^n/\text{Spec}(k)} \cong \Omega^1_{\mathbb{A}^n/\text{Spec}(k)}is a free module, \textbf{RHom}(i^*\mathbf{L}_{\mathbb{A}^n/\text{Spec}(k)},\mathcal{O}_{X_0}[+1]) = 0. Also, because \mathbf{L}_{X_0/\mathbb{A}^n} \cong \mathcal{I}/\mathcal{I}^2[+1] , there are isomorphisms\begin{align}
