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Abstract:

Let k be an infinite field, A the polynomial ring k[x1 , . . . , xn] and F ∈ AN×M a matrix such that Im F ⊂ AN A-free (in particular, Quillen-Suslin Theorem implies that Ker F is also free). Let D be the maximum of the degrees of the entries of F and s the rank of F. We show that there exists a basis {v1 , . . . , vM} of AM such that {v1 , . . . , vM-s} is a basis of Ker F, {F(vM-s+1), . . . , F(vM)} is a basis of Im F and the degrees of their coordinates are of order ((M - s)sD)O(n4). This result allows to obtain a single exponential degree upper bound for a basis of the coordinate ring of a reduced complete intersection variety in Noether position.

Registro:

Documento: Artículo
Título:On the degrees of bases of free modules over a polynomial ring
Autor:Almeida, M.; D'Alfonso, L.; Solerno, P.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Depto. de Economía y Matemat., Universidad de San Andrés, Vito Dumas 284, 1644 Victoria, Buenos Aires, Argentina
Año:1999
Volumen:231
Número:4
Página de inicio:679
Página de fin:706
DOI: http://dx.doi.org/10.1007/PL00004746
Título revista:Mathematische Zeitschrift
Título revista abreviado:Math. Z.
ISSN:00255874
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v231_n4_p679_Almeida

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Citas:

---------- APA ----------
Almeida, M., D'Alfonso, L. & Solerno, P. (1999) . On the degrees of bases of free modules over a polynomial ring. Mathematische Zeitschrift, 231(4), 679-706.
http://dx.doi.org/10.1007/PL00004746
---------- CHICAGO ----------
Almeida, M., D'Alfonso, L., Solerno, P. "On the degrees of bases of free modules over a polynomial ring" . Mathematische Zeitschrift 231, no. 4 (1999) : 679-706.
http://dx.doi.org/10.1007/PL00004746
---------- MLA ----------
Almeida, M., D'Alfonso, L., Solerno, P. "On the degrees of bases of free modules over a polynomial ring" . Mathematische Zeitschrift, vol. 231, no. 4, 1999, pp. 679-706.
http://dx.doi.org/10.1007/PL00004746
---------- VANCOUVER ----------
Almeida, M., D'Alfonso, L., Solerno, P. On the degrees of bases of free modules over a polynomial ring. Math. Z. 1999;231(4):679-706.
http://dx.doi.org/10.1007/PL00004746