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Amadou Lamine Fall
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, 59 no. 3 (2009), p. 1015-1027, doi: 10.5802/aif.2455
Article PDF | Reviews MR 2543660 | Zbl 1173.13021
Class. Math.: 14H50, 14Q20, 13D02
Keywords: Castelnuovo-Mumford regularity, singular shemes, singular locus
[1] A. Bertram, L. Ein & R. Lazarsfeld, “Vanishing theorem , a theorem of Severi,and the equations defining projectives varieties”, J. Amer. Math. Soc. 4 (1991), p. 587-602 Article | MR 1092845 | Zbl 0762.14012
[2] G. Caviglia & E. Sbarra, “Characteristic-free bounds for the Castelnuovo-Mumford regularity”, Compositio Math. 141 (2005), p. 1365-1373 Article | MR 2188440 | Zbl 1100.13020
[3] M. Chardin, “Regularity of ideals and their powers”, Prépublication(institut de mathématiques de Jussieu), 364, 2004
[4] M. Chardin, A. L. Fall & U. Nagel, “Bounds for the Castelnuovo-Mumford regularity of modules”, Math. Z. 258 (2008), p. 69-80 Article | MR 2350034 | Zbl 1138.13007
[5] M. Chardin & G. Moreno-Socias, “Regularity of lex-segment ideals : some closed formulas and applications”, Proc. Amer. Math. Soc. 131 (2003), p. 1093-1102 Article | MR 1948099 | Zbl 1036.13014
[6] M. Chardin & B. Ulrich, “Liaison and the Castelnuovo-Mumford regularity”, Amer. J. Math. 124 (2002), p. 1103-1124 Article | MR 1939782 | Zbl 1029.14016
[7] H. Flenner, L. O’Carroll & W. Vogel, Joins and Intersections, Springer Monographs in Mathematics (New York), 1999 MR 1724388 | Zbl 0939.14003
[8] G. Kempf, F. Knudsen, D. Mumford & S. Donat, Toroidal Embeddings, Lecture Notes in Math. (Springer-Verlag New York), 1973 Zbl 0271.14017
[9] Sjögren, “On the regularity of graded $k$-algebras of Krull dimension $\le 1$”, Math. Scand. 71 (1992), p. 167-171 Article | MR 1212701 | Zbl 0791.13004
[10] K. Smith, “F-rational rings have rational singularities”, Amer. J. Math. 119 (1997), p. 159-180 Article | MR 1428062 | Zbl 0910.13004
Amadou Lamine Fall
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, 59 no. 3 (2009), p. 1015-1027, doi: 10.5802/aif.2455
Article PDF | Reviews MR 2543660 | Zbl 1173.13021
Class. Math.: 14H50, 14Q20, 13D02
Keywords: Castelnuovo-Mumford regularity, singular shemes, singular locus
Résumé - Abstract
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.
Bibliography
[2] G. Caviglia & E. Sbarra, “Characteristic-free bounds for the Castelnuovo-Mumford regularity”, Compositio Math. 141 (2005), p. 1365-1373 Article | MR 2188440 | Zbl 1100.13020
[3] M. Chardin, “Regularity of ideals and their powers”, Prépublication(institut de mathématiques de Jussieu), 364, 2004
[4] M. Chardin, A. L. Fall & U. Nagel, “Bounds for the Castelnuovo-Mumford regularity of modules”, Math. Z. 258 (2008), p. 69-80 Article | MR 2350034 | Zbl 1138.13007
[5] M. Chardin & G. Moreno-Socias, “Regularity of lex-segment ideals : some closed formulas and applications”, Proc. Amer. Math. Soc. 131 (2003), p. 1093-1102 Article | MR 1948099 | Zbl 1036.13014
[6] M. Chardin & B. Ulrich, “Liaison and the Castelnuovo-Mumford regularity”, Amer. J. Math. 124 (2002), p. 1103-1124 Article | MR 1939782 | Zbl 1029.14016
[7] H. Flenner, L. O’Carroll & W. Vogel, Joins and Intersections, Springer Monographs in Mathematics (New York), 1999 MR 1724388 | Zbl 0939.14003
[8] G. Kempf, F. Knudsen, D. Mumford & S. Donat, Toroidal Embeddings, Lecture Notes in Math. (Springer-Verlag New York), 1973 Zbl 0271.14017
[9] Sjögren, “On the regularity of graded $k$-algebras of Krull dimension $\le 1$”, Math. Scand. 71 (1992), p. 167-171 Article | MR 1212701 | Zbl 0791.13004
[10] K. Smith, “F-rational rings have rational singularities”, Amer. J. Math. 119 (1997), p. 159-180 Article | MR 1428062 | Zbl 0910.13004
© Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310