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http://hdl.handle.net/2445/192861
Title: | The representation type of determinantal varieties |
Author: | Kleppe, Jan O. Miró-Roig, Rosa M. (Rosa Maria) |
Keywords: | Varietats (Matemàtica) Teoria de mòduls Àlgebra homològica Anells associatius Manifolds (Mathematics) Moduli theory Homological algebra Associative rings |
Issue Date: | 25-Feb-2017 |
Publisher: | Springer Verlag |
Abstract: | This work is entirely devoted to construct huge families of indecomposable arithmetically Cohen-Macaulay (resp. Ulrich) sheaves $\mathcal{E}$ of arbitrary high rank on a general standard (resp. linear) determinantal scheme $X \subset \mathbb{P}^n$ of codimension $c \geq 1, n-c \geq 1$ and defined by the maximal minors of a $t \times(t+c-1)$ homogeneous matrix $\mathcal{A}$. The sheaves $\mathcal{E}$ are constructed as iterated extensions of sheaves of lower rank. As applications: (1) we prove that any general standard determinantal scheme $X \subset \mathbb{P}^n$ is of wild representation type provided the degrees of the entries of the matrix $\mathcal{A}$ satisfy some weak numerical assumptions; and (2) we determine values of $t, n$ and $n-c$ for which a linear standard determinantal scheme $X \subset \mathbb{P}^n$ 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s10468-017-9673-4 |
It is part of: | Algebras And Representation Theory, 2017, vol. 20, num. 4, p. 1029-1059 |
URI: | http://hdl.handle.net/2445/192861 |
Related resource: | https://doi.org/10.1007/s10468-017-9673-4 |
ISSN: | 1386-923X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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