On Castelnuovo's regularity and Hilbert functions
Compositio Mathematica, Tome 76 (1990) no. 1-2, pp. 265-275.
@article{CM_1990__76_1-2_265_0,
author = {Nagel, Uwe},
title = {On Castelnuovo's regularity and Hilbert functions},
journal = {Compositio Mathematica},
pages = {265--275},
volume = {76},
number = {1-2},
year = {1990},
zbl = {0726.13011},
mrnumber = {1078866},
language = {en},
url = {archive.numdam.org/item/CM_1990__76_1-2_265_0/}
}
Nagel, Uwe. On Castelnuovo's regularity and Hilbert functions. Compositio Mathematica, Tome 76 (1990) no. 1-2, pp. 265-275. http://archive.numdam.org/item/CM_1990__76_1-2_265_0/

[1] E. Ballico, On the defining equations of subvarieties in Pn. Boll. Un. Mat. Ital. A(6) 5 (1986) 243-246. | MR 850294 | Zbl 0601.14041

[2] D. Bayer and M. Stillman, On the complexity of computing syzygies. J. Symbolic Comput. 6 (1988) 135-147. | MR 988409 | Zbl 0667.68053

[3] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity. J. Algebra 88 (1984) 89-133. | MR 741934 | Zbl 0531.13015

[4] H. Flenner, Die Sätze von Bertini für lokale Ringe. Math. Ann. 229 (1977) 97-111. | MR 460317 | Zbl 0398.13013

[5] V.A. Greenberg, A Castelnuovo bound for projective varieties admitting a stable linear projection onto a hypersurface. Thesis, Columbia university, 1987.

[6] L. Gruson, R. Lazarsfeld and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves. Invent. Math. 72 (1983) 491-506. | MR 704401 | Zbl 0565.14014

[7] J. Harris (with the collaboration of D. Eisenbud), Curves in projective space. Les presses de l'Université, Montréal 1982. | MR 685427

[8] L.T. Hoa, A note on projective monomial surfaces. Math. Nachr. (to appear). | MR 1138379 | Zbl 0765.14019

[9] R. Lazarsfeld, A sharp Castelnuovo bound for smooth surfaces. Duke Math. J. 55 (1987) 423-429. | MR 894589 | Zbl 0646.14005

[10] D. Mumford, Lectures on curves on an algebraic surface. Ann of Math. Studies 59, Princeton Univ. Press, Princeton, N.J., 1966. | MR 209285 | Zbl 0187.42701

[11] U. Nagel, Castelnuovo-Regularität und Hilbertreihen. Math. Nachr. 142 (1989) 27-43. | MR 1017370 | Zbl 0688.13008

[12] U. Nagel and W. Vogel, Bounds for Castelnuovo's regularity and the genus of projective varieties. In: Topics in Algebra. Banach Center Publications, Volume 26. PWN-Polish Scientific Publishers, Warsaw 1989 (to appear). | MR 1171267 | Zbl 0735.14032

[13] A. Ooishi, Castelnuovo's regularity of graded rings and modules. Hiroshima Math. J. 12 (1982) 627-644. | MR 676563 | Zbl 0557.13007

[14] A. Ooishi, Genera and arithmetic genera of commutative rings. Hiroshima Math. J. 17 (1987) 47-66. | MR 886981 | Zbl 0625.13015

[15] P. Philippon, Lemmes de zéros dans les groupes algébriques commutatifs. Bull. Soc. math. France 114 (1986) 355-383. | Numdam | MR 878242 | Zbl 0617.14001

[16] P. Quartararo Jr. and H.S. Butts, Finite unions of ideals and modules. Proc. Amer. Math. Soc. 52 (1975) 91-96. | MR 382249 | Zbl 0315.13001

[17] J. Rathmann, The uniform position principle for curves in characteristic p. Math. Ann. 276 (1987) 565-579. | MR 879536 | Zbl 0595.14041

[18] J. Rathmann, On the completeness of linear series cut out by hypersurfaces. Preprint, M.I.T., June 1988.

[19] J.-P. Serre, Faisceaus algébriques cohérents. Ann. of Math. 61 (1955) 197-278. | MR 68874 | Zbl 0067.16201

[20] J. Stückrad and W. Vogel, Buchsbaum rings and applications. Springer, Berlin 1986. | MR 881220 | Zbl 0606.13018

[21] J. Stückrad and W. Vogel, Castelnuovo bounds for certain subvarieties in Pn. Math. Ann. 276 (1987), 341-352. | MR 870972 | Zbl 0628.14037

[22] J. Stückrad and W. Vogel, Castelnuovo bounds for locally Cohen-Macaulay schemes. Math. Nachr. 136 (1988), 307-320. | MR 952482 | Zbl 0662.14027

[23] J. Stückrad and W. Vogel, Castelnuovo's regularity and cohomological properties of sets of points in Pn. Math. Ann. 284 (1989) 487-501. | MR 1001716 | Zbl 0652.14007

[24] N.V. Trung and L.T. Hoa, Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. Amer. Math. Soc. 298 (1986) 145-167. | MR 857437 | Zbl 0631.13020

[25] W. Vogel, Letter to D. Eisenbud dated 5 October, 1987.

[26] U. Nagel and W. Vogel, Castelnuovo's regularity of graded k-algebras and applications. Stud. Cerc. Mat. (in preparation).