Artículo
Botbol, N. "The implicitization problem for φ{symbol} : Pn (P1)n + 1" (2009) Journal of Algebra. 322(11):3878-3895
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Abstract:
We develop in this paper methods for studying the implicitization problem for a rational map φ{symbol} : Pn (P1)n + 1 defining a hypersurface in (P1)n + 1, based on computing the determinant of a graded strand of a Koszul complex. We show that the classical study of Macaulay resultants and Koszul complexes coincides, in this case, with the approach of approximation complexes and we study and give a geometric interpretation for the acyclicity conditions. Under suitable hypotheses, these techniques enable us to obtain the implicit equation, up to a power, and up to some extra factor. We give algebraic and geometric conditions for determining when the computed equation defines the scheme theoretic image of φ{symbol}, and, what are the extra varieties that appear. We also give some applications to the problem of computing sparse discriminants. © 2009 Elsevier Inc. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | The implicitization problem for φ{symbol} : Pn (P1)n + 1 |
| Autor: | Botbol, N. |
| Filiación: | Departamento de Matemática, FCEN, Universidad de Buenos Aires, Argentina Institut de Mathématiques de Jussieu, Université de P. et M. Curie, Paris VI, France |
| Palabras clave: | Approximation complex; Elimination theory; Implicitization; Koszul complex; Rational map; Syzygy |
| Año: | 2009 |
| Volumen: | 322 |
| Número: | 11 |
| Página de inicio: | 3878 |
| Página de fin: | 3895 |
| DOI: | http://dx.doi.org/10.1016/j.jalgebra.2009.03.006 |
| Título revista: | Journal of Algebra |
| Título revista abreviado: | J. Algebra |
| ISSN: | 00218693 |
| CODEN: | JALGA |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v322_n11_p3878_Botbol.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v322_n11_p3878_Botbol |
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Citas:
---------- APA ----------
(2009) . The implicitization problem for φ{symbol} : Pn (P1)n + 1. Journal of Algebra, 322(11), 3878-3895.http://dx.doi.org/10.1016/j.jalgebra.2009.03.006
---------- CHICAGO ----------
Botbol, N. "The implicitization problem for φ{symbol} : Pn (P1)n + 1" . Journal of Algebra 322, no. 11 (2009) : 3878-3895.http://dx.doi.org/10.1016/j.jalgebra.2009.03.006
---------- MLA ----------
Botbol, N. "The implicitization problem for φ{symbol} : Pn (P1)n + 1" . Journal of Algebra, vol. 322, no. 11, 2009, pp. 3878-3895.http://dx.doi.org/10.1016/j.jalgebra.2009.03.006
---------- VANCOUVER ----------
Botbol, N. The implicitization problem for φ{symbol} : Pn (P1)n + 1. J. Algebra. 2009;322(11):3878-3895.http://dx.doi.org/10.1016/j.jalgebra.2009.03.006
