The representation type of determinantal varieties
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/192861 |
| Acceso en línea: | https://hdl.handle.net/2445/192861 |
| Access Level: | acceso abierto |
| Palabra clave: | Varietats (Matemàtica) Teoria de mòduls Àlgebra homològica Anells associatius Manifolds (Mathematics) Moduli theory Homological algebra Associative rings |
| Sumario: | 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. |
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