Non-arithmetically Cohen–Macaulay schemes of wild representation type

The main goal of this short paper is to prove that any non-arithmetically Cohen–Macaulay polarized scheme \((X,\mathscr {O}_X(1))\) of dimension \({{\mathrm{dim}}}(X)\ge 2\), under mild conditions on \(\mathscr {O}_X(1)\), supports arbitrarily large families of non-isomorphic indecomposable aCM vector bundles with respect to \(\mathscr {O}_X(l)\), \(l\ge 3\). Namely, they are of wild representation type.