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.