En:
J. Algebra 2009;322(11):3878-3895
Fecha:
2009
Formato:
application/pdf
Tipo de documento:
info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion
Descriptores:
Descripción:
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.
Identificador(es):
Derechos:
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
http://creativecommons.org/licenses/by/2.5/ar
Descargar texto: paper_00218693_v322_n11_p3878_Botbol.oai
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Cita bibliográfica:
Botbol, N. (2009). The implicitization problem for φ{symbol} : Pn (P1)n + 1 (info:eu-repo/semantics/article). [consultado: ] Disponible en el Repositorio Digital Institucional de la Universidad de Buenos Aires: <http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&cl=CL1&d=paper_00218693_v322_n11_p3878_Botbol_oai>