Compactifications of rational maps, and the implicit equations of their images
In this paper, we give different compactifications for the domain and the codomain of an affine rational map f which parameterizes a hypersurface. We show that the closure of the image of this map (with possibly some other extra hypersurfaces) can be represented by a matrix of linear syzygies. We co...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/16543 |
| Acceso en línea: | http://hdl.handle.net/11336/16543 |
| Access Level: | acceso abierto |
| Palabra clave: | Rational Maps Implicitization Syzygies https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper, we give different compactifications for the domain and the codomain of an affine rational map f which parameterizes a hypersurface. We show that the closure of the image of this map (with possibly some other extra hypersurfaces) can be represented by a matrix of linear syzygies. We compactify A n−1 into an (n − 1)- dimensional projective arithmetically Cohen–Macaulay subscheme of some P N . One particular interesting compactification of A n−1 is the toric variety associated to the Newton polytope of the polynomials defining f . We consider two different compactifications for the codomain of f : P n and (P 1 ) n . In both cases we give sufficient conditions, in terms of the nature of the base locus of the map, for getting a matrix representation of its closed image, without involving extra hypersurfaces. This constitutes a direct generalization of the corresponding results established by Laurent Busé and Jean-Pierre Jouanolou (2003) [12], Laurent Busé et al. (2009) [9], Laurent Busé and Marc Dohm (2007) [11], Nicolás Botbol et al. (2009) [5] and Nicolás Botbol (2009). |
|---|