The Representation Type of Determinantal Varieties

作者：Kleppe Jan O; Miro Roig Rosa M^*

来源：Algebras and Representation Theory, 2017, 20(4): 1029-1059.

DOI：10.1007/s10468-017-9673-4

• Ulrich bundles
• Determinantal varieties
• Representation type
• Wild representation type

This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves of arbitrary high rank on a general standard (resp. linear) determinantal scheme of codimension c >= 1, n - c >= 1 and defined by the maximal minors of a t x (t + c-1) homogeneous matrix . The sheaves are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme is of wild representation type provided the degrees of the entries of the matrix satisfy some weak numerical assumptions; and (2) we determine values of t, n and n - c for which a linear standard determinantal scheme 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.

• 出版日期2017-8