Families of determinantal schemes
Given integers $ a_0\le a_1\le \cdots \le a_{t+c-2}$ and $ b_1\le \cdots \le b_t$, we denote by $ W(\underline{b};\underline{a})\subset \textrm{Hilb}^p(\mathbb{P}^{n})$ the locus of good determinantal schemes $ X\subset \mathbb{P}^{n}$ of codimension $ c$ defined by the maximal minors of a $ t\times...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2011 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/96593 |
| Acesso em linha: | https://hdl.handle.net/2445/96593 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Àlgebra Esquemes (Geometria algebraica) Algebra Schemes (Algebraic geometry) |
| Resumo: | Given integers $ a_0\le a_1\le \cdots \le a_{t+c-2}$ and $ b_1\le \cdots \le b_t$, we denote by $ W(\underline{b};\underline{a})\subset \textrm{Hilb}^p(\mathbb{P}^{n})$ the locus of good determinantal schemes $ X\subset \mathbb{P}^{n}$ of codimension $ c$ defined by the maximal minors of a $ t\times (t+c-1)$ homogeneous matrix with entries homogeneous polynomials of degree $ a_j-b_i$. The goal of this paper is to extend and complete the results given by the authors in an earlier paper and determine under weakened numerical assumptions the dimension of $ W(\underline{b};\underline{a})$ as well as whether the closure of $ W(\underline{b};\underline{a})$ is a generically smooth irreducible component of $ \textrm{Hilb}^p(\mathbb{P}^{n})$. |
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