Codimension 2 subschemes of projective spaces with stable restricted tangent bundle and liaison classes (Q1392973)

Let \(C\subset \mathbb{P}^n\) be a smooth complex curve. Using several results and methods from linkage theory we show first how to construct, in any even linkage class, many curves in \(\mathbb{P}^3\) such that \(T\mathbb{P}^3 \mid C\) is stable. Then a corresponding result is given for even linkage classes of codimension 2 locally Cohen-Macaulay subschemes of \(\mathbb{P}^n\). Here is our main result: Theorem. Assume \(\mathbb{P}^n= \mathbb{P}^n_{\mathbf K}\) where \({\mathbf K}\) is an algebraically closed field of characteristic 0. Let \({\mathbf L}= {\mathbf L}_0 \cup {\mathbf L}_1 \cup {\mathbf L}_2 \cup \cdots\) be an even linkage class of equidimensional codimension 2 locally Cohen-Macaulay subschemes of \(\mathbb{P}^n\) (decomposed in the usual way with respect to shift). Then there is an integer \(x\) such that for all integers \(t\geq x\) there is an integral locally Cohen-Macaulay subscheme \(X_t\in {\mathcal L}_t\) with \(\dim (\text{Sing} (X))\leq n-6\) and with \(T\mathbb{P}^n \mid X_t\) stable.