n-dimensional Fano varieties of wild representation type

Abstract

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

Cited by in corpus (1)

• Representations of Clifford algebras of ternary quartic forms