The Representation Type of Determinantal Varieties

This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves E of arbitrary high rank on a general standard (resp. linear) determinantal scheme X ⊂ ℙ n of codimension c ≥ 1, n − c ≥ 1 and defined by the maximal minors of a t × ( t + c −1) homogeneous matrix A . The sheaves E are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme X ⊂ ℙ n is of wild representation type provided the degrees of the entries of the matrix A satisfy some weak numerical assumptions; and (2) we determine values of t , n and n − c for which a linear standard determinantal scheme X ⊂ ℙ n is of wild representation type with respect to the much more restrictive category of its indecomposable Ulrich sheaves, i.e. X is of Ulrich wild representation type.