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Comptes Rendus Mathématique
Volume 341, n° 4
pages 233-238 (août 2005)
Doi : 10.1016/j.crma.2005.06.020
Received : 13 April 2005 ;  accepted : 7 June 2005
Sur la régularité de Castelnuovo-Mumford des idéaux, en dimension 2
On the Castelnuovo-Mumford regularity of ideals, in dimension 2
 

Marc Chardin a , Amadou Lamine Fall b
a Institut de mathématiques de Jussieu, CNRS et université Paris VI, 4, place Jussieu, 75005 Paris, France 
b Département de mathématiques, faculté des sciences, université Cheikh Anta Diop, Dakar, Sénégal 

Résumé

Nous montrons une borne pour la régularité de Castelnuovo-Mumford dʼun idéal homogène I dʼun anneau de polynômes A en termes du nombre de variables et des degrés des générateurs dans le cas où la dimension de   est au plus deux. Cette borne améliore celle obtenue par Caviglia et Sbarra dans [G. Caviglia, E. Sbarra, Characteristic-free bounds for the Castelnuovo-Mumford regularity, Prépublication, math.AC/0310122]. Puis, en sʼinspirant de lʼarticle Chardin et DʼCruz [M. Chardin, C. DʼCruz, Castelnuovo-Mumford regularity: examples of curves and surface, J. Algebra 270 (2003) 347-360], nous construisons à partir de familles de courbes monomiales des idéaux homogènes ayant une régularité proche des bornes fournies précédemment. Pour citer cet article : M. Chardin, A.L. Fall, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

We give a bound on the Castelnuovo-Mumford regularity of a homogeneous ideal I , in a polynomial ring A , in terms of the number of variables and the degrees of generators, when the dimension of   is at most two. This bound improves the one obtained by Caviglia and Sbarra in [G. Caviglia, E. Sbarra, Characteristic-free bounds for the Castelnuovo-Mumford regularity, Prépublication, math.AC/0310122]. In the continuation of the examples constructed in Chardin and DʼCruz [M. Chardin, C. DʼCruz, Castelnuovo-Mumford regularity: examples of curves and surface, J. Algebra 270 (2003) 347-360], we use families of monomial curves to construct homogeneous ideals showing that these bounds are quite sharp. To cite this article: M. Chardin, A.L. Fall, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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