Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses  [ Bounds for the Castelnuovo-Mumford regularity of singular schemes ]
Annales de l'Institut Fourier, Volume 59 (2009) no. 3, p. 1015-1027

We establish bounds for the Castelnuovo-Mumford regularity of singular scheme, in terms of the degrees of the equations defining the scheme and of the dimension of the singular locus. In the case where the singularities are isolated, we improve the bound given by Chardin and Ulrich, and in the general case we establish a bound doubly exponential in the dimension of the singular locus.

Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.

DOI : https://doi.org/10.5802/aif.2455
Classification:  14H50,  14Q20,  13D02
Keywords: Castelnuovo-Mumford regularity, singular shemes, singular locus
@article{AIF_2009__59_3_1015_0,
     author = {Fall, Amadou Lamine},
     title = {Bornes pour la r\'egularit\'e de Castelnuovo-Mumford des sch\'emas non lisses},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {3},
     year = {2009},
     pages = {1015-1027},
     doi = {10.5802/aif.2455},
     mrnumber = {2543660},
     zbl = {1173.13021},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2009__59_3_1015_0}
}
Fall, Amadou Lamine. Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses. Annales de l'Institut Fourier, Volume 59 (2009) no. 3, pp. 1015-1027. doi : 10.5802/aif.2455. http://www.numdam.org/item/AIF_2009__59_3_1015_0/

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