A sharp bound for the regularity index of fat points in general position

Catalisano, M. V.; Trung, N. V.; Valla, G.

doi:10.1090/S0002-9939-1993-1146859-0

A sharp bound for the regularity index of fat points in general position
HTML articles powered by AMS MathViewer

by M. V. Catalisano, N. V. Trung and G. Valla PDF

Proc. Amer. Math. Soc. 118 (1993), 717-724 Request permission

Abstract:

A bound is given for the regularity index of the coordinate ring of a set of fat points in general position in ${\mathbf {P}}_k^n$. The bound is attained by points on a rational normal curve.

References

J. Alexander, Singularités imposables en position générale à une hypersurface projective, Compositio Math. 68 (1988), no. 3, 305–354 (French). MR 971330

Ricerche generali sopra i sistemi lineari di curve piane

42

M. V. Catalisano, Linear systems of plane curves through fixed “fat” points of $\textbf {P}^2$, J. Algebra 142 (1991), no. 1, 81–100. MR 1125206, DOI 10.1016/0021-8693(91)90218-W
Maria Virginia Catalisano, “Fat” points on a conic, Comm. Algebra 19 (1991), no. 8, 2153–2168. MR 1123117, DOI 10.1080/00927879108824252
Maria Virginia Catalisano and Silvio Greco, Linear systems: developments of some results by F. Enriques and B. Segre, Geometry and complex variables (Bologna, 1988/1990) Lecture Notes in Pure and Appl. Math., vol. 132, Dekker, New York, 1991, pp. 41–57. MR 1151633
E. D. Davis and A. V. Geramita, The Hilbert function of a special class of $1$-dimensional Cohen-Macaulay graded algebras, The curves seminar at Queen’s, Vol. III (Kingston, Ont., 1983) Queen’s Papers in Pure and Appl. Math., vol. 67, Queen’s Univ., Kingston, ON, 1984, pp. Exp. No. H, 29. MR 783099
Alessandro Gimigliano, Regularity of linear systems of plane curves, J. Algebra 124 (1989), no. 2, 447–460. MR 1011606, DOI 10.1016/0021-8693(89)90142-7

Our thin knowledge on fat points

83

Silvio Greco, Remarks on the postulation of zero-dimensional subschemes of projective space, Math. Ann. 284 (1989), no. 2, 343–351. MR 1000115, DOI 10.1007/BF01442880
Brian Harbourne, Complete linear systems on rational surfaces, Trans. Amer. Math. Soc. 289 (1985), no. 1, 213–226. MR 779061, DOI 10.1090/S0002-9947-1985-0779061-2
André Hirschowitz, La méthode d’Horace pour l’interpolation à plusieurs variables, Manuscripta Math. 50 (1985), 337–388 (French, with English summary). MR 784148, DOI 10.1007/BF01168836
Beniamino Segre, Alcune questioni su insiemi finiti di punti in geometria algebrica. , Atti Convegno Internaz. Geometria Algebrica (Torino, 1961) Rattero, Turin, 1962, pp. 15–33 (Italian). MR 0146714