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The aim of this work is to provide the first examples of $n$-dimensionalvarieties of wild representation type, for arbitrary $n\geq 2$. More precisely,we prove that all Fano blow-ups of $\PP^n$ at a finite number of points are ofwild representation type exhibiting families of dimension of order $r^2$ ofsimple (hence, indecomposable) ACM rank $r$ vector bundles for any $r\geq n$.In the two dimensional case, the vector bundles that we construct are moreoverUlrich bundles and $\mu$-stable with respect to certain ample divisor.

n-dimensional Fano varieties of wild representation type